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## Berndt, Bruce Carl

Compute Distance To:
 Author ID: berndt.bruce-c Published as: Berndt, B. C.; Berndt, Bruce; Berndt, Bruce C. Homepage: https://faculty.math.illinois.edu/~berndt/ External Links: MGP · Math-Net.Ru · Wikidata · dblp · GND
 Documents Indexed: 277 Publications since 1967, including 35 Books
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#### Serials

 13 The Ramanujan Journal 12 American Mathematical Monthly 12 Transactions of the American Mathematical Society 11 Acta Arithmetica 11 Proceedings of the American Mathematical Society 9 Advances in Mathematics 9 Journal für die Reine und Angewandte Mathematik 8 Journal of Number Theory 6 Glasgow Mathematical Journal 6 International Journal of Number Theory 4 Illinois Journal of Mathematics 4 Journal of the London Mathematical Society. Second Series 4 Mathematische Annalen 4 Proceedings of the Edinburgh Mathematical Society. Series II 4 Annals of Combinatorics 3 Mathematical Proceedings of the Cambridge Philosophical Society 3 Rocky Mountain Journal of Mathematics 3 Bulletin of the London Mathematical Society 3 Journal of Combinatorial Theory. Series A 3 Journal of Computational and Applied Mathematics 3 Memoirs of the American Mathematical Society 3 Bulletin of the American Mathematical Society 3 Contemporary Mathematics 3 Progress in Mathematics 2 Journal of Mathematical Analysis and Applications 2 Mathematics Magazine 2 Canadian Mathematical Bulletin 2 Indian Journal of Mathematics 2 Journal of Approximation Theory 2 The Journal of the Indian Mathematical Society. New Series 2 Mathematische Zeitschrift 2 Pacific Journal of Mathematics 2 Advances in Applied Mathematics 2 Journal of the Ramanujan Mathematical Society 2 IMRN. International Mathematics Research Notices 2 Aequationes Mathematicae 2 L’Enseignement Mathématique. 2e Série 2 SIAM Journal on Mathematical Analysis 2 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 2 Notices of the American Mathematical Society 2 RIMS Kokyuroku 2 South East Asian Journal of Mathematics and Mathematical Sciences 2 Publications de la Faculté d’Électrotechnique de l’Université à Belgrade. Série Mathématiques et Physique 2 History of Mathematics (Providence) 2 Ramanujan Mathematical Society Lecture Notes Series 1 Applicable Analysis 1 The Mathematical Intelligencer 1 Canadian Journal of Mathematics 1 Duke Mathematical Journal 1 Ganita 1 Journal of the Korean Mathematical Society 1 The Mathematics Student 1 Mathematika 1 Monatshefte für Mathematik 1 Nagoya Mathematical Journal 1 Results in Mathematics 1 International Journal of Mathematics 1 Elemente der Mathematik 1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 1 Bulletin of the American Mathematical Society. New Series 1 Expositiones Mathematicae 1 Indagationes Mathematicae. New Series 1 Mathematical Research Letters 1 Séminaire Lotharingien de Combinatoire 1 Acta Mathematica Sinica. English Series 1 The Quarterly Journal of Mathematics 1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 1 Nordisk Matematisk Tidskrift 1 Canadian Mathematical Society Series of Monographs and Advanced Texts 1 Student Mathematical Library 1 Developments in Mathematics 1 Culture and History of Mathematics 1 1 Monographs in Number Theory 1 Mathematics Newsletter 1 Trends in Mathematics
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#### Fields

 237 Number theory (11-XX) 104 Special functions (33-XX) 42 History and biography (01-XX) 33 Combinatorics (05-XX) 22 Sequences, series, summability (40-XX) 20 General and overarching topics; collections (00-XX) 11 Approximations and expansions (41-XX) 8 Functions of a complex variable (30-XX) 4 Algebraic geometry (14-XX) 4 Numerical analysis (65-XX) 2 Integral transforms, operational calculus (44-XX) 1 Real functions (26-XX) 1 Mathematics education (97-XX)

#### Citations contained in zbMATH Open

205 Publications have been cited 3,652 times in 2,162 Documents Cited by Year
Ramanujan’s notebooks. Part III. Zbl 0733.11001
Berndt, Bruce C.
1991
Gauss and Jacobi sums. Zbl 0906.11001
Berndt, Bruce C.; Evans, Ronald J.; Williams, Kenneth S.
1998
Ramanujan’s notebooks. Part I. Zbl 0555.10001
Berndt, Bruce C.
1985
Number theory in the spirit of Ramanujan. Zbl 1117.11001
Berndt, Bruce C.
2006
Ramanujan’s lost notebook. I. Zbl 1075.11001
Andrews, George E.; Berndt, Bruce C.
2005
Ramanujan’s notebooks. Part II. Zbl 0716.11001
Berndt, Bruce C.
1989
Ramanujan’s notebooks. Part V. Zbl 0886.11001
Berndt, Bruce C.
1998
Ramanujan’s notebooks. Part IV. Zbl 0785.11001
Berndt, Bruce C.
1994
Ramanujan’s lost notebook. Part II. Zbl 1180.11001
Andrews, George E.; Berndt, Bruce C.
2009
Ramanujan’s theories of elliptic functions to alternative bases. Zbl 0843.33012
Berndt, Bruce C.; Bhargava, S.; Garvan, Frank G.
1995
On the Hurwitz zeta-function. Zbl 0229.10023
Berndt, Bruce C.
1972
Ramanujan: Letters and commentary. Zbl 0842.01026
Berndt, Bruce C.; Rankin, Robert A.
1995
Analytic Eisenstein series, theta-functions, and series relations in the spirit of Ramanujan. Zbl 0384.10011
Berndt, Bruce C.
1978
Chapter 16 of Ramanujan’s second notebook: Theta-functions and q-series. Zbl 0565.33002
Adiga, C.; Berndt, Bruce C.; Bhargava, S.; Watson, G. N.
1985
Gauss, Landen, Ramanujan, the arithmetic-geometric mean, ellipses, $$\pi$$ , and the Ladies Diary. Zbl 0665.26007
Almkvist, Gert; Berndt, Bruce C.
1988
Ramanujan’s series for $$1/\pi$$: a survey. Zbl 1229.11162
Baruah, Deka Nayandeep; Berndt, Bruce C.; Chan, Huat Heng
2009
Modular transformations and generalizations of several formulae of Ramanujan. Zbl 0365.10021
Berndt, Bruce C.
1977
The determination of Gauss sums. Zbl 0471.10028
Berndt, Bruce C.; Evans, Ronald J.
1981
Sums of Gauss, Jacobi, and Jacobsthal. Zbl 0412.10027
Berndt, Bruce C.; Evans, Ronald J.
1979
The number of zeros for $$\zeta^{(k)}(s)$$. Zbl 0203.35503
Berndt, Bruce C.
1970
The continued fractions found in the unorganized portions of Ramanujan’s notebooks. Zbl 0758.40001
Andrews, George E.; Berndt, Bruce C.; Jacobsen, Lisa; Lamphere, Robert L.
1992
Explicit evaluations and reciprocity theorems for finite trigonometric sums. Zbl 1011.11057
Berndt, Bruce C.; Yeap, Boon Pin
2002
Character analogues of the Poisson and Euler-MacLaurin summation formulas with applications. Zbl 0316.10023
Berndt, Bruce C.
1975
Partition identities and Ramanujan’s modular equations. Zbl 1206.11132
Baruah, Nayandeep Deka; Berndt, Bruce C.
2007
Ramanujan’s lost notebook. Part IV. Zbl 1288.11002
Andrews, George E.; Berndt, Bruce C.
2013
Ramanujan’s lost notebook. Part III. Zbl 1248.11003
Andrews, George E.; Berndt, Bruce C.
2012
Reciprocity theorems for Dedekind sums and generalizations. Zbl 0342.10014
Berndt, Bruce C.
1977
Eisenstein series and Ramanujan-type series for $$1 / \pi$$. Zbl 1204.33005
Baruah, Nayandeep Deka; Berndt, Bruce C.
2010
Ramanujan’s forty identities for the Rogers-Ramanujan functions. Zbl 1118.11044
Berndt, Bruce C.; Choi, Geumlan; Choi, Youn-Seo; Hahn, Heekyoung; Yeap, Boon Pin; Yee, Ae Ja; Yesilyurt, Hamza; Yi, Jinhee
2007
Analytic properties of arithmetic sums arising in the theory of the classical theta-functions. Zbl 0537.10006
Berndt, Bruce C.; Goldberg, Larry A.
1984
Classical theorems on quadratic residues. Zbl 0337.10031
Berndt, Bruce C.
1976
Generalized Dedekind eta-functions and generalized Dedekind sums. Zbl 0262.10015
Berndt, Bruce C.
1973
Identities involving the coefficients of a class of Dirichlet series. I,II. Zbl 0175.32802
Berndt, Bruce C.
1969
Finite trigonometric sums and class numbers. Zbl 1099.11039
Berndt, Bruce C.; Zaharescu, Alexandru
2004
Explicit evaluations of the Rogers-Ramanujan continued fraction. Zbl 0862.33017
Berndt, Bruce C.; Chan, Heng Huat; Zhang, Liang-Cheng
1996
Some values for the Rogers-Ramanujan continued fraction. Zbl 0838.33011
Berndt, Bruce C.; Chan, Heng Huat
1995
Dedekind sums and a paper of G. H. Hardy. Zbl 0319.10006
Berndt, Bruce C.
1976
Periodic analogues of the Euler-Maclaurin and Poisson summation formulas with applications to number theory. Zbl 0268.10008
Berndt, Bruce C.; Schoenfeld, Lowell
1974
Asymptotic expansions of certain partial theta functions. Zbl 1272.11057
Berndt, Bruce C.; Kim, Byungchan
2011
Ramanujan’s unpublished manuscript on the partition and tau functions with proofs and commentary. Zbl 0932.11002
Berndt, Bruce C.; Ono, Ken
1999
Ramanujan’s series for $$1/\pi$$ arising from his cubic and quartic theories of elliptic functions. Zbl 1139.11023
Baruah, Nayandeep Deka; Berndt, Bruce C.
2008
Partition-theoretic interpretations of certain modular equations of Schröter, Russell, and Ramanujan. Zbl 1131.05008
Berndt, Bruce C.
2007
On Ramanujan’s quartic theory of elliptic functions. Zbl 1005.33009
Berndt, Bruce C.; Chan, Heng Huat; Liaw, Wen-Chin
2001
Generalized Eisenstein series and modified Dedekind sums. Zbl 0294.10018
Berndt, Bruce C.
1975
Hecke’s theory of modular forms and Dirichlet series. Zbl 1202.11030
Berndt, Bruce C.; Knopp, Marvin I.
2008
The Rogers-Ramanujan continued fraction. Zbl 0953.11005
Berndt, Bruce C.; Chan, Heng Huat; Huang, Sen-Shan; Kang, Soon-Yi; Sohn, Jaebum; Son, Seung Hwan
1999
Ramanujan’s notebooks. Zbl 0389.10002
Berndt, Bruce C.
1978
Ramanujan’s lost notebook: combinatorial proofs of identities associated with Heine’s transformation or partial theta functions. Zbl 1227.05053
Berndt, Bruce C.; Kim, Byungchan; Yee, Ae Ja
2010
Sums of Gauß, Eisenstein, Jacobi, Jacobsthal, and Brewer. Zbl 0393.12029
Berndt, Bruce C.; Evans, Ronald J.
1979
Sixth order mock theta functions. Zbl 1122.33010
Berndt, Bruce C.; Chan, Song Heng
2007
A certain quotient of eta-functions found in Ramanujan’s lost notebook. Zbl 1054.11022
Berndt, Bruce C.; Chan, Heng Huat; Kang, Soon-Yi; Zhang, Liang-Cheng
2002
On the Brocard-Ramanujan Diophantine equation $$n! + 1 = m^2$$. Zbl 0999.11078
Berndt, Bruce C.; Galway, William F.
2000
Character transformation formulae similar to those for the Dedekind eta- function. Zbl 0265.10016
Berndt, Bruce C.
1973
A reciprocity theorem for certain $$q$$-series found in Ramanujan’s lost notebook. Zbl 1123.33012
Berndt, Bruce C.; Chan, Song Heng; Yeap, Boon Pin; Yee, Ae Ja
2007
Cranks and dissections in Ramanujan’s lost notebook. Zbl 1114.11082
Berndt, Bruce C.; Chan, Heng Huat; Chan, Song Heng; Liaw, Wen-Chin
2005
A new identity for $$(q;q)_\infty^{10}$$ with an application to Ramanujan’s partition congruence modulo 11. Zbl 1060.11063
Berndt, Bruce C.; Chan, Song Heng; Liu, Zhi-Guo; Yesilyurt, Hamza
2004
Formulas of Ramanujan for the power series coefficients of certain quotients of Eisenstein series. Zbl 1033.11019
Berndt, Bruce C.; Bialek, Paul R.; Yee, Ae Ja
2002
Some theorems on the Rogers-Ramanujan continued fraction in Ramanujan’s lost notebook. Zbl 1037.11011
Berndt, Bruce C.; Huang, Sen-Shan; Sohn, Jaebum; Son, Seung Hwan
2000
Elementary evaluation of $$\zeta(2n)$$. Zbl 0303.10038
Berndt, Bruce C.
1975
Partition identities arising from theta function identities. Zbl 1154.11036
Baruah, Nayandeep Deka; Berndt, Bruce C.
2008
The problems submitted by Ramanujan to the Journal of the Indian Mathematical Society. Zbl 1133.11300
Berndt, Bruce C.; Choi, Youn-Seo; Kang, Soon-Yi
1999
Ramanujan’s class invariants and cubic continued fraction. Zbl 0843.11007
Berndt, Bruce C.; Chan, Heng Huat; Zhang, Liang-Cheng
1995
On Eisenstein series with characters and the values of Dirichlet L-functions. Zbl 0279.10023
Berndt, Bruce C.
1975
Circle and divisor problems, and double series of Bessel functions. Zbl 1326.11059
Berndt, Bruce C.; Kim, Sun; Zaharescu, Alexandru
2013
Ramanujan and the modular $$j$$-invariant. Zbl 0990.11022
Berndt, Bruce C.; Chan, Heng Huat
1999
Ramanujan’s identities for Eta-functions. Zbl 0737.11008
Berndt, Bruce C.; Zhang, Liang-Cheng
1992
On a secant Dirichlet series and Eichler integrals of Eisenstein series. Zbl 1402.11060
Berndt, Bruce C.; Straub, Armin
2016
Koshliakov’s formula and Guinand’s formula in Ramanujan’s lost notebook. Zbl 1183.33007
Berndt, Bruce C.; Lee, Yoonbok; Sohn, Jaebum
2008
Weighted divisor sums and Bessel function series. Zbl 1100.33001
Berndt, Bruce C.; Zaharescu, Alexandru
2006
On the parity of partition functions. Zbl 1047.11098
Berndt, Bruce C.; Yee, Ae Ja; Zaharescu, Alexandru
2003
Combinatorial proofs of identities in Ramanujan’s lost notebook associated with the Rogers-Fine identity and false theta functions. Zbl 1037.05005
Berndt, Bruce C.; Yee, Ae Ja
2003
Ramanujan’s remarkable product of theta-functions. Zbl 0901.33007
Berndt, Bruce C.; Chan, Heng Huat; Zhang, Liang-Cheng
1997
Ramanujan’s class invariants, Kronecker’s limit formula, and modular equations. Zbl 0885.11058
Berndt, Bruce C.; Chan, Heng Huat; Zhang, Liang-Cheng
1997
Chapter 12 of Ramanujan’s second notebook: Continued fractions. Zbl 0589.33002
Berndt, Bruce C.; Lamphere, Robert L.; Wilson, B. M.
1985
Sums involving the greatest integer function and Riemann-Stieltjes integration. Zbl 0487.10002
Berndt, Bruce C.; Dieter, Ulrich
1982
Identities involving the coefficients of a class of Dirichlet series. V. Zbl 0228.10024
Berndt, Bruce C.
1971
On the average order of a class of arithmetical functions. II. Zbl 0219.10050
Berndt, Bruce C.
1971
Weighted divisor sums and Bessel function series. II. Zbl 1236.33010
Berndt, Bruce C.; Kim, Sun; Zaharescu, Alexandru
2012
A transformation formula involving the gamma and Riemann zeta functions in Ramanujan’s lost notebook. Zbl 1322.11086
Berndt, Bruce C.; Dixit, Atul
2010
Modular equations in Ramanujan’s Lost Notebook. Zbl 0989.11021
Berndt, Bruce C.
2000
On the average order of a class of arithmetical functions. I. Zbl 0216.31303
Berndt, Bruce C.
1971
Identities involving the coefficients of a class of Dirichlet series. III. Zbl 0191.33003
Berndt, Bruce C.
1969
Proofs of conjectures of Sandon and Zanello on colored partition identities. Zbl 1315.11092
Berndt, Bruce C.; Zhou, Roberta R.
2014
Weighted divisor sums and Bessel function series. III. Zbl 1326.11057
Berndt, Bruce C.; Kim, Sun; Zaharescu, Alexandru
2013
Determinations of analogues of Gauss sums and other trigonometric sums. Zbl 1088.11064
Beck, Matthias; Berndt, Bruce C.; Chan, O-Yeat; Zaharescu, Alexandru
2005
On Ramanujan’s continued fraction for $$(q^2;q^3)_{\infty}/(q;q^3)_{\infty}$$. Zbl 1063.33026
Andrews, George E.; Berndt, Bruce C.; Sohn, Jaebum; Yee, Ae Ja; Zaharescu, Alexandru
2003
Eisenstein series and approximations to $$\pi$$. Zbl 0998.33003
Berndt, Bruce C.; Chan, Heng Huat
2001
Ramanujan’s short unpublished manuscript on integrals and series related to Euler’s constant. Zbl 0964.40004
Berndt, Bruce C.; Bowman, Douglas C.
2000
Eisenstein series in Ramanujan’s Lost Notebook. Zbl 1024.11026
Berndt, Bruce C.; Chan, Heng Huat; Sohn, Jaebum; Son, Seung Hwan
2000
Ramanujan’s theory of theta-functions. Zbl 0801.11024
Berndt, Bruce C.
1993
Periodic Bernoulli numbers, summation formulas and applications. Zbl 0326.10016
Berndt, Bruce C.
1975
Two new proofs of Lerch’s functional equation. Zbl 0235.10020
Berndt, Bruce C.
1972
New pathways and connections in number theory and analysis motivated by two incorrect claims of Ramanujan. Zbl 1396.11103
Berndt, Bruce C.; Dixit, Atul; Roy, Arindam; Zaharescu, Alexandru
2017
Identities for partitions with distinct colors. Zbl 1386.11127
Berndt, Bruce C.; Zhou, Roberta R.
2015
Ramanujan’s Eisenstein series and new hypergeometric-like series for $$1/\pi ^{2}$$. Zbl 1185.33002
Baruah, Nayandeep Deka; Berndt, Bruce C.
2009
A page on Eisenstein series in Ramanujan’s Lost Notebook. Zbl 1090.11025
Berndt, Bruce C.; Yee, Ae Ja
2003
Flowers which we connot yet see growing in Ramanujan’s garden of hypergeometric series, elliptic functions, and $$q$$’s. Zbl 1014.33012
Berndt, Bruce C.
2001
Ramanujan: essays and surveys. Zbl 1117.11002
Berndt, Bruce C. (ed.); Rankin, Robert A. (ed.)
2001
Incomplete elliptic integrals in Ramanujan’s lost notebook. Zbl 0971.33012
Berndt, Bruce C.; Chan, Heng Huat; Huang, Sen-Shan
2000
The gamma function and the Hurwitz zeta-function. Zbl 0565.10036
Berndt, Bruce C.
1985
Four identities for third order mock theta functions. Zbl 1455.11136
Andrews, George E.; Berndt, Bruce C.; Chan, Song Heng; Kim, Sun; Malik, Amita
2020
Ramanujan’s lost notebook. Part V. Zbl 1416.11001
Andrews, George E.; Berndt, Bruce C.
2018
Partitions into $$k$$th powers of terms in an arithmetic progression. Zbl 1412.11129
Berndt, Bruce C.; Malik, Amita; Zaharescu, Alexandru
2018
The circle problem of Gauss and the divisor problem of Dirichlet – still unsolved. Zbl 1396.11001
Berndt, Bruce C.; Kim, Sun; Zaharescu, Alexandru
2018
Sums of squares and products of Bessel functions. Zbl 1451.11024
Berndt, Bruce C.; Dixit, Atul; Kim, Sun; Zaharescu, Alexandru
2018
New pathways and connections in number theory and analysis motivated by two incorrect claims of Ramanujan. Zbl 1396.11103
Berndt, Bruce C.; Dixit, Atul; Roy, Arindam; Zaharescu, Alexandru
2017
On a theorem of A. I. Popov on sums of squares. Zbl 1422.11077
Berndt, Bruce C.; Dixit, Atul; Kim, Sun; Zaharescu, Alexandru
2017
On a secant Dirichlet series and Eichler integrals of Eisenstein series. Zbl 1402.11060
Berndt, Bruce C.; Straub, Armin
2016
Integrals associated with Ramanujan and elliptic functions. Zbl 1354.33015
Berndt, Bruce C.
2016
Identities for partitions with distinct colors. Zbl 1386.11127
Berndt, Bruce C.; Zhou, Roberta R.
2015
Logarithmic means and double series of Bessel functions. Zbl 1390.11100
Berndt, Bruce C.; Kim, Sun
2015
Weighted divisor sums and Bessel function series. V. Zbl 1326.33007
Berndt, Bruce C.; Kim, Sun; Zaharescu, Alexandru
2015
Proofs of conjectures of Sandon and Zanello on colored partition identities. Zbl 1315.11092
Berndt, Bruce C.; Zhou, Roberta R.
2014
Analogues of Koshliakov’s formula. Zbl 1308.33004
Berndt, Bruce C.; Kim, Sun; Zaharescu, Alexandru
2014
Ramanujan’s lost notebook. Part IV. Zbl 1288.11002
Andrews, George E.; Berndt, Bruce C.
2013
Circle and divisor problems, and double series of Bessel functions. Zbl 1326.11059
Berndt, Bruce C.; Kim, Sun; Zaharescu, Alexandru
2013
Weighted divisor sums and Bessel function series. III. Zbl 1326.11057
Berndt, Bruce C.; Kim, Sun; Zaharescu, Alexandru
2013
The circle and divisor problems, and Ramanujan’s contributions through Bessel function series. Zbl 1360.11093
Berndt, Bruce C.; Kim, Sun; Zaharescu, Alexandru
2013
Dirichlet $$L-$$functions, elliptic curves, hypergeometric functions, and rational approximation with partial sums of power series. Zbl 1297.11082
Berndt, Bruce C.; Kim, Sun; Zaharescu, Alexandru
2013
Diophantine approximation of the exponential function and Sondow’s conjecture. Zbl 1292.11079
Berndt, Bruce C.; Kim, Sun; Zaharescu, Alexandru
2013
Diophantine approximation with partial sums of power series. Zbl 1318.11088
Berndt, Bruce C.; Kim, Sun; Phaovibul, M. Tip; Zaharescu, Alexandru
2013
Ramanujan’s lost notebook. Part III. Zbl 1248.11003
Andrews, George E.; Berndt, Bruce C.
2012
Weighted divisor sums and Bessel function series. II. Zbl 1236.33010
Berndt, Bruce C.; Kim, Sun; Zaharescu, Alexandru
2012
Weighted divisor sums and Bessel function series. IV. Zbl 1270.11098
Berndt, Bruce C.; Kim, Sun; Zaharescu, Alexandru
2012
Two-dimensional series evaluations via the elliptic functions of Ramanujan and Jacobi. Zbl 1290.11112
Berndt, Bruce C.; Lamb, George; Rogers, Mathew
2012
Ramanujan’s elementary method in partition congruences. Zbl 1263.11094
Berndt, Bruce C.; Gugg, Chadwick; Kim, Sun
2012
Two Dirichlet series evaluations found on page 196 of Ramanujan’s lost notebook. Zbl 1275.11116
Berndt, Bruce C.; Chan, Heng Huat; Tanigawa, Yoshio
2012
Asymptotic expansions of certain partial theta functions. Zbl 1272.11057
Berndt, Bruce C.; Kim, Byungchan
2011
Character analogues of theorems of Ramanujan, Koshliakov and Guinand. Zbl 1216.33012
Berndt, Bruce C.; Dixit, Atul; Sohn, Jaebum
2011
The chief accountant and mathematical friend of Ramanujan – S. Narayana Aiyar. Zbl 1226.01017
Berndt, Bruce C.
2011
On sums of powers in Ramanujan’s lost notebook. Zbl 1232.11025
Berndt, Bruce C.; Schultz, Daniel
2011
Eisenstein series and Ramanujan-type series for $$1 / \pi$$. Zbl 1204.33005
Baruah, Nayandeep Deka; Berndt, Bruce C.
2010
Ramanujan’s lost notebook: combinatorial proofs of identities associated with Heine’s transformation or partial theta functions. Zbl 1227.05053
Berndt, Bruce C.; Kim, Byungchan; Yee, Ae Ja
2010
A transformation formula involving the gamma and Riemann zeta functions in Ramanujan’s lost notebook. Zbl 1322.11086
Berndt, Bruce C.; Dixit, Atul
2010
What is a $$q$$-series? Zbl 1245.33013
Berndt, Bruce C.
2010
A proof of the general theta transformation formula. Zbl 1343.11048
Berndt, Bruce C.; Gugg, Chadwick; Kongsiriwong, Sarachai; Thiel, Johann
2010
Cranks—really, the final problem. Zbl 1206.11001
Berndt, Bruce C.; Chan, Heng Huat; Chan, Song Heng; Liaw, Wen-Chin
2010
Ramanujan’s lost notebook. Part II. Zbl 1180.11001
Andrews, George E.; Berndt, Bruce C.
2009
Ramanujan’s series for $$1/\pi$$: a survey. Zbl 1229.11162
Baruah, Deka Nayandeep; Berndt, Bruce C.; Chan, Huat Heng
2009
Ramanujan’s Eisenstein series and new hypergeometric-like series for $$1/\pi ^{2}$$. Zbl 1185.33002
Baruah, Nayandeep Deka; Berndt, Bruce C.
2009
An integral analogue of theta functions and Gauss sums in Ramanujan’s lost notebook. Zbl 1196.11113
Berndt, Bruce C.; Xu, Ping
2009
A reciprocity theorem for certain hypergeometric series. Zbl 1287.33001
Berndt, Bruce C.; Koukoulopoulos, Dimitris
2009
Ramanujan’s series for $$1/\pi$$ arising from his cubic and quartic theories of elliptic functions. Zbl 1139.11023
Baruah, Nayandeep Deka; Berndt, Bruce C.
2008
Hecke’s theory of modular forms and Dirichlet series. Zbl 1202.11030
Berndt, Bruce C.; Knopp, Marvin I.
2008
Partition identities arising from theta function identities. Zbl 1154.11036
Baruah, Nayandeep Deka; Berndt, Bruce C.
2008
Koshliakov’s formula and Guinand’s formula in Ramanujan’s lost notebook. Zbl 1183.33007
Berndt, Bruce C.; Lee, Yoonbok; Sohn, Jaebum
2008
Your hit parade: the top ten most fascinating formulas in Ramanujan’s lost notebook. Zbl 1153.33300
Andrews, George E.; Berndt, Bruce C.
2008
Questionable claims found in Ramanujan’s lost notebook. Zbl 1163.11002
Berndt, Bruce C.; Chan, O-Yeat; Lim, Sung-Geun; Zaharescu, Alexandru
2008
Partition identities and Ramanujan’s modular equations. Zbl 1206.11132
Baruah, Nayandeep Deka; Berndt, Bruce C.
2007
Ramanujan’s forty identities for the Rogers-Ramanujan functions. Zbl 1118.11044
Berndt, Bruce C.; Choi, Geumlan; Choi, Youn-Seo; Hahn, Heekyoung; Yeap, Boon Pin; Yee, Ae Ja; Yesilyurt, Hamza; Yi, Jinhee
2007
Partition-theoretic interpretations of certain modular equations of Schröter, Russell, and Ramanujan. Zbl 1131.05008
Berndt, Bruce C.
2007
Sixth order mock theta functions. Zbl 1122.33010
Berndt, Bruce C.; Chan, Song Heng
2007
A reciprocity theorem for certain $$q$$-series found in Ramanujan’s lost notebook. Zbl 1123.33012
Berndt, Bruce C.; Chan, Song Heng; Yeap, Boon Pin; Yee, Ae Ja
2007
Ramanujan’s congruences for the partition function modulo 5, 7, and 11. Zbl 1197.11137
Berndt, Bruce C.
2007
An identity for the Dedekind eta-function involving two independent complex variables. Zbl 1123.11015
Berndt, Bruce C.; Hart, William B.
2007
Solving Ramanujan’s differential equations for Eisenstein series via a first order Riccati equation. Zbl 1145.11035
Hill, James M.; Berndt, Bruce C.; Huber, Tim
2007
Preface: a special issue in celebration of Marvin Knopp’s 73rd birthday. Zbl 1197.01051
Berndt, Bruce C.; Choie, YoungJu
2007
Number theory in the spirit of Ramanujan. Zbl 1117.11001
Berndt, Bruce C.
2006
Weighted divisor sums and Bessel function series. Zbl 1100.33001
Berndt, Bruce C.; Zaharescu, Alexandru
2006
Ramanujan’s lost notebook. I. Zbl 1075.11001
Andrews, George E.; Berndt, Bruce C.
2005
Cranks and dissections in Ramanujan’s lost notebook. Zbl 1114.11082
Berndt, Bruce C.; Chan, Heng Huat; Chan, Song Heng; Liaw, Wen-Chin
2005
Determinations of analogues of Gauss sums and other trigonometric sums. Zbl 1088.11064
Beck, Matthias; Berndt, Bruce C.; Chan, O-Yeat; Zaharescu, Alexandru
2005
Continued fractions with three limit points. Zbl 1131.11311
Andrews, George E.; Berndt, Bruce C.; Sohn, Jaebum; Yee, Ae Ja; Zaharescu, Alexandru
2005
New identities for the Rogers-Ramanujan functions. Zbl 1205.11113
Berndt, Bruce C.; Yesilyurt, Hamza
2005
Ramanujan and cranks. Zbl 1219.33017
Berndt, Bruce C.; Chan, Heng Huat; Chan, Song Heng; Liawt, Wen-Chin
2005
On the power series coefficients of certain quotients of Eisenstein series. Zbl 1145.11312
Berndt, Bruce C.; Bialek, Paul R.
2005
Finite trigonometric sums and class numbers. Zbl 1099.11039
Berndt, Bruce C.; Zaharescu, Alexandru
2004
A new identity for $$(q;q)_\infty^{10}$$ with an application to Ramanujan’s partition congruence modulo 11. Zbl 1060.11063
Berndt, Bruce C.; Chan, Song Heng; Liu, Zhi-Guo; Yesilyurt, Hamza
2004
New theorems on the parity of partition functions. Zbl 1034.11059
Berndt, Bruce C.; Yee, Ae Ja; Zaharescu, Alexandru
2004
An unpublished manuscript of Ramanujan on infinite series identities. Zbl 1066.40001
Berndt, Bruce C.
2004
$$q$$-Gauss summation via Ramanujan and combinatorics. Zbl 1063.33027
Berndt, Bruce C.; Yee, Ae Ja
2004
On the parity of partition functions. Zbl 1047.11098
Berndt, Bruce C.; Yee, Ae Ja; Zaharescu, Alexandru
2003
Combinatorial proofs of identities in Ramanujan’s lost notebook associated with the Rogers-Fine identity and false theta functions. Zbl 1037.05005
Berndt, Bruce C.; Yee, Ae Ja
2003
On Ramanujan’s continued fraction for $$(q^2;q^3)_{\infty}/(q;q^3)_{\infty}$$. Zbl 1063.33026
Andrews, George E.; Berndt, Bruce C.; Sohn, Jaebum; Yee, Ae Ja; Zaharescu, Alexandru
2003
A page on Eisenstein series in Ramanujan’s Lost Notebook. Zbl 1090.11025
Berndt, Bruce C.; Yee, Ae Ja
2003
On the generalized Rogers–Ramanujan continued fraction. Zbl 1040.11053
Berndt, Bruce C.; Yee, Ae Ja
2003
A quasi-theta product in Ramanujan’s lost notebook. Zbl 1055.11015
Berndt, Bruce C.; Chan, Heng Huat; Zaharescu, Alexandru
2003
The life and work of R. A. Rankin (1915–2001). Zbl 1039.01011
Berndt, Bruce C.; Kohnen, Winfried; Ono, Ken
2003
Theorems on partitions from a page in Ramanujan’s lost notebook. Zbl 1031.11062
Berndt, Bruce C.; Yee, Ae Ja; Yi, Jinhee
2003
Explicit evaluations and reciprocity theorems for finite trigonometric sums. Zbl 1011.11057
Berndt, Bruce C.; Yeap, Boon Pin
2002
A certain quotient of eta-functions found in Ramanujan’s lost notebook. Zbl 1054.11022
Berndt, Bruce C.; Chan, Heng Huat; Kang, Soon-Yi; Zhang, Liang-Cheng
2002
Formulas of Ramanujan for the power series coefficients of certain quotients of Eisenstein series. Zbl 1033.11019
Berndt, Bruce C.; Bialek, Paul R.; Yee, Ae Ja
2002
Integrals of Eisenstein series and derivatives of $$L$$-functions. Zbl 1086.11023
Ahlgren, Scott; Berndt, Bruce C.; Yee, Ae Ja; Zaharescu, Alexandru
2002
Congruences for the coefficients of quotients of Eisenstein series. Zbl 1018.11020
Berndt, Bruce C.; Yee, Ae Ja
2002
Ramanujan’s contributions to Eisenstein series, especially in his Lost Notebook. Zbl 1241.11107
Berndt, Bruce C.; Yee, Ae Ja
2002
An integral of Dedekind $$\eta$$-functions in Ramanujan’s lost notebook. Zbl 1001.11017
Berndt, Bruce C.; Zaharescu, Alexandru
2002
Number theory for the millennium I. Proceedings of the millennial conference on number theory, Urbana-Champaign, IL, USA, May 21–26, 2000. Zbl 1002.00005
Bennett, M. A. (ed.); Berndt, B. C. (ed.); Boston, N. (ed.); Diamond, H. G. (ed.); Hildebrand, A. J. (ed.); Philipp, W. (ed.)
2002
Asymptotic formulas for two continued fractions in Ramanujan’s Lost Notebook. Zbl 1034.11008
Berndt, Bruce C.; Sohn, Jaebum
2002
On Ramanujan’s quartic theory of elliptic functions. Zbl 1005.33009
Berndt, Bruce C.; Chan, Heng Huat; Liaw, Wen-Chin
2001
Eisenstein series and approximations to $$\pi$$. Zbl 0998.33003
Berndt, Bruce C.; Chan, Heng Huat
2001
Flowers which we connot yet see growing in Ramanujan’s garden of hypergeometric series, elliptic functions, and $$q$$’s. Zbl 1014.33012
Berndt, Bruce C.
2001
Ramanujan: essays and surveys. Zbl 1117.11002
Berndt, Bruce C. (ed.); Rankin, Robert A. (ed.)
2001
On the transformation formula for the Dedekind eta-function. Zbl 1040.11028
Berndt, Bruce C.; Venkatachaliengar, K.
2001
On the Brocard-Ramanujan Diophantine equation $$n! + 1 = m^2$$. Zbl 0999.11078
Berndt, Bruce C.; Galway, William F.
2000
Some theorems on the Rogers-Ramanujan continued fraction in Ramanujan’s lost notebook. Zbl 1037.11011
Berndt, Bruce C.; Huang, Sen-Shan; Sohn, Jaebum; Son, Seung Hwan
2000
Modular equations in Ramanujan’s Lost Notebook. Zbl 0989.11021
Berndt, Bruce C.
2000
Ramanujan’s short unpublished manuscript on integrals and series related to Euler’s constant. Zbl 0964.40004
Berndt, Bruce C.; Bowman, Douglas C.
2000
Eisenstein series in Ramanujan’s Lost Notebook. Zbl 1024.11026
Berndt, Bruce C.; Chan, Heng Huat; Sohn, Jaebum; Son, Seung Hwan
2000
Incomplete elliptic integrals in Ramanujan’s lost notebook. Zbl 0971.33012
Berndt, Bruce C.; Chan, Heng Huat; Huang, Sen-Shan
2000
The books studied by Ramanujan in India. Zbl 1012.01008
Berndt, Bruce C.; Rankin, Robert A.
2000
...and 105 more Documents
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#### Cited by 1,781 Authors

 71 Berndt, Bruce Carl 34 Saikia, Nipen 33 Baruah, Nayandeep Deka 32 Chan, Heng Huat 32 Zaharescu, Alexandru 29 Mahadeva Naika, Megadahalli Sidda 28 Cooper, Shaun 28 Evans, Ronald J. 28 Xia, Ernest X. W. 25 Dixit, Atul 24 Kim, Byungchan 22 Sun, Zhihong 20 Qiu, Songliang 20 Yao, Olivia Xiang Mei 19 Chan, Song Heng 19 Chu, Yuming 18 Alkan, Emre 18 Andrews, George Eyre 18 Chu, Wenchang 18 Liu, Zhi-Guo 18 Lovejoy, Jeremy 18 Williams, Kenneth S. 18 Xu, Ce 17 Wang, Liuquan 16 Bringmann, Kathrin 16 Chen, Chaoping 16 Lin, Bernard L. S. 16 Mc Laughlin, James G. 16 Zudilin, Wadim 15 Adiga, Chandrashekar 15 Gu, Nancy Shan Shan 15 Yee, Ae Ja 14 Borwein, Jonathan Michael 14 Coffey, Mark William 14 Srivastava, Hari Mohan 14 Vasuki, Kaliyur Ranganna 13 Chen, William Yong-Chuan 13 Guillera, Jesús 13 Sun, Zhi-Wei 13 Toh, Pee Choon 12 Barman, Rupam 12 Eie, Minking 12 Feng, Tao 12 Mao, Renrong 12 Momihara, Koji 12 Sills, Andrew V. 12 Simsek, Yilmaz 12 Wang, Miaokun 12 Ye, Dongxi 12 Zhang, Wenpeng 11 Chern, Shane 11 Cui, Su-Ping 11 Garvan, Frank G. 11 Huber, Tim 11 Jennings-Shaffer, Chris 11 Kanemitsu, Shigeru 11 Rogers, Mathew D. 11 Roy, Arindam 11 Vuorinen, Matti Keijo Kustaa 11 Xiang, Qing 11 Yue, Qin 10 Berkovich, Alexander 10 Can, Mumun 10 Cvijović, Djurdje 10 Dilcher, Karl 10 Folsom, Amanda 10 Li, Chengju 10 Moll, Victor Hugo 10 Ono, Ken 10 Tang, Dazhao 9 Bowman, Douglas C. 9 Chan, Heichi 9 Hirschhorn, Michael D. 9 Kang, Soon-Yi 9 Kostov, Vladimir Petrov 9 Merca, Mircea 9 Mortenson, Eric T. 9 Sellers, James Allen 9 Sohn, Jaebum 9 Straub, Armin 8 Alaca, Ayşe 8 Alaca, Şaban 8 Alzer, Horst 8 El Bachraoui, Mohamed 8 Guo, Victor J. W. 8 Ma, Xiaoyan 8 Milas, Antun 8 Paris, Richard Bruce 8 Tsumura, Hirofumi 8 Yesilyurt, Hamza 8 Zhou, Yajun 7 Adell, José Antonio 7 Baoulina, Ioulia N. 7 Bhuvan, E. N. 7 Boruah, Chayanika 7 Flajolet, Philippe 7 Kim, Daeyeoul 7 Kim, Sun I. 7 Kumar, Belakavadi Radhakrishna Srivatsa 7 Liaw, Wen-Chin ...and 1,681 more Authors
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#### Cited in 295 Serials

 281 The Ramanujan Journal 220 Journal of Number Theory 137 Journal of Mathematical Analysis and Applications 124 International Journal of Number Theory 67 Proceedings of the American Mathematical Society 47 Advances in Mathematics 37 Finite Fields and their Applications 35 Transactions of the American Mathematical Society 31 Journal of Combinatorial Theory. Series A 29 Mathematics of Computation 29 Journal of Computational and Applied Mathematics 29 Advances in Applied Mathematics 26 Rocky Mountain Journal of Mathematics 26 Applied Mathematics and Computation 25 Research in Number Theory 23 Bulletin of the Australian Mathematical Society 23 Discrete Mathematics 23 Results in Mathematics 23 Integral Transforms and Special Functions 21 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 20 Integers 18 Annals of Combinatorics 17 Functiones et Approximatio. Commentarii Mathematici 17 Designs, Codes and Cryptography 16 Indian Journal of Pure & Applied Mathematics 16 Acta Mathematica Sinica. English Series 13 Journal de Théorie des Nombres de Bordeaux 12 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 12 Acta Arithmetica 12 International Journal of Mathematics and Mathematical Sciences 12 Journal of Approximation Theory 12 Mathematische Zeitschrift 12 Proceedings of the Japan Academy. Series A 10 American Mathematical Monthly 10 Abstract and Applied Analysis 10 Science China. Mathematics 9 Mathematische Annalen 9 Monatshefte für Mathematik 9 European Journal of Combinatorics 9 Turkish Journal of Mathematics 9 Journal of the Australian Mathematical Society 8 Communications in Mathematical Physics 8 Lithuanian Mathematical Journal 8 Mathematical Notes 8 Proceedings of the Edinburgh Mathematical Society. Series II 8 Journal of High Energy Physics 8 Advances in Difference Equations 8 Cryptography and Communications 8 Afrika Matematika 7 Israel Journal of Mathematics 7 Journal of Mathematical Physics 7 Mathematical Proceedings of the Cambridge Philosophical Society 7 Duke Mathematical Journal 7 Manuscripta Mathematica 7 Experimental Mathematics 7 Journal of Difference Equations and Applications 7 Computational Methods and Function Theory 7 South East Asian Journal of Mathematics and Mathematical Sciences 7 Annali dell’Università di Ferrara. Sezione VII. Scienze Matematiche 7 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 6 Archiv der Mathematik 6 Czechoslovak Mathematical Journal 6 Linear Algebra and its Applications 6 Indagationes Mathematicae. New Series 6 Journal of Algebraic Combinatorics 6 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 6 Journal of Integer Sequences 6 Comptes Rendus. Mathématique. Académie des Sciences, Paris 6 Journal of Classical Analysis 5 The Mathematical Gazette 5 The Mathematical Intelligencer 5 Acta Mathematica Vietnamica 5 Nagoya Mathematical Journal 5 Tokyo Journal of Mathematics 5 Journal of the Ramanujan Mathematical Society 5 Journal of Mathematical Sciences (New York) 5 Honam Mathematical Journal 4 Computers & Mathematics with Applications 4 Ukrainian Mathematical Journal 4 Glasgow Mathematical Journal 4 Journal of Algebra 4 Journal of Combinatorial Theory. Series B 4 Journal für die Reine und Angewandte Mathematik 4 Mathematika 4 Bulletin of the Korean Mathematical Society 4 Applied Mathematics Letters 4 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 4 Journal of Inequalities and Applications 4 Communications of the Korean Mathematical Society 4 Proceedings of the Steklov Institute of Mathematics 4 Research in the Mathematical Sciences 4 Electronic Research Archive 3 Analysis Mathematica 3 International Journal of Mathematical Education in Science and Technology 3 Problems of Information Transmission 3 Annales de l’Institut Fourier 3 Compositio Mathematica 3 Journal of the Korean Mathematical Society 3 Journal of the London Mathematical Society. Second Series 3 Matematički Vesnik ...and 195 more Serials
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#### Cited in 55 Fields

 1,695 Number theory (11-XX) 711 Special functions (33-XX) 467 Combinatorics (05-XX) 93 Functions of a complex variable (30-XX) 90 Sequences, series, summability (40-XX) 73 Algebraic geometry (14-XX) 65 Approximations and expansions (41-XX) 61 Numerical analysis (65-XX) 59 Real functions (26-XX) 53 Information and communication theory, circuits (94-XX) 39 Quantum theory (81-XX) 34 Harmonic analysis on Euclidean spaces (42-XX) 30 Probability theory and stochastic processes (60-XX) 23 History and biography (01-XX) 22 Computer science (68-XX) 20 Ordinary differential equations (34-XX) 17 Field theory and polynomials (12-XX) 17 Linear and multilinear algebra; matrix theory (15-XX) 17 Nonassociative rings and algebras (17-XX) 14 Difference and functional equations (39-XX) 13 Integral transforms, operational calculus (44-XX) 12 Partial differential equations (35-XX) 12 Geometry (51-XX) 11 Statistical mechanics, structure of matter (82-XX) 10 Group theory and generalizations (20-XX) 10 Manifolds and cell complexes (57-XX) 9 Functional analysis (46-XX) 8 Global analysis, analysis on manifolds (58-XX) 7 Several complex variables and analytic spaces (32-XX) 6 Relativity and gravitational theory (83-XX) 5 Dynamical systems and ergodic theory (37-XX) 4 General and overarching topics; collections (00-XX) 4 Abstract harmonic analysis (43-XX) 4 Convex and discrete geometry (52-XX) 4 Differential geometry (53-XX) 4 Statistics (62-XX) 4 Biology and other natural sciences (92-XX) 3 Measure and integration (28-XX) 3 Operator theory (47-XX) 3 Mathematics education (97-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Commutative algebra (13-XX) 2 $$K$$-theory (19-XX) 2 Topological groups, Lie groups (22-XX) 1 Mathematical logic and foundations (03-XX) 1 Category theory; homological algebra (18-XX) 1 Potential theory (31-XX) 1 Integral equations (45-XX) 1 Algebraic topology (55-XX) 1 Mechanics of particles and systems (70-XX) 1 Mechanics of deformable solids (74-XX) 1 Fluid mechanics (76-XX) 1 Optics, electromagnetic theory (78-XX) 1 Operations research, mathematical programming (90-XX) 1 Systems theory; control (93-XX)

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