Luca, Florian; Mabaso, Sibusiso; Stănică, Pantelimon On the prime factors of the iterates of the Ramanujan \(\tau\)-function. (English) Zbl 07298494 Proc. Edinb. Math. Soc., II. Ser. 63, No. 4, 1031-1047 (2020). MSC: 11B39 11J86 PDF BibTeX XML Cite \textit{F. Luca} et al., Proc. Edinb. Math. Soc., II. Ser. 63, No. 4, 1031--1047 (2020; Zbl 07298494) Full Text: DOI
Matiyasevich, Yuri Computational aspects of Hamburger’s theorem. (English) Zbl 07218081 Fillion, Nicolas (ed.) et al., Algorithms and complexity in mathematics, epistemology, and science. Proceedings of 2015 and 2016 ACMES conferences, London, UK. Selected papers. New York, NY: Springer; Toronto: The Fields Institute for Research in the Mathematical Sciences (ISBN 978-1-4939-9050-4/hbk; 978-1-4939-9051-1/ebook). Fields Institute Communications 82, 195-223 (2019). Reviewer: Stelian Mihalas (Timişoara) MSC: 11M06 11Y99 PDF BibTeX XML Cite \textit{Y. Matiyasevich}, Fields Inst. Commun. 82, 195--223 (2019; Zbl 07218081) Full Text: DOI
Luca, Florian; Mabaso, Sibusiso Diophantine equations with the Ramanujan \(\tau\) function of factorials, Fibonacci numbers, and Catalan numbers. (English) Zbl 07099365 Fibonacci Q. 57, No. 3, 255-259 (2019). Reviewer: Mahadi Ddamulira (Kampala) MSC: 11B83 11B39 11B65 PDF BibTeX XML Cite \textit{F. Luca} and \textit{S. Mabaso}, Fibonacci Q. 57, No. 3, 255--259 (2019; Zbl 07099365) Full Text: Link
Chaubey, Sneha; Koutsaki, K. Paolina; Zaharescu, Alexandru Monotonicity properties of \(L\)-functions. (English) Zbl 1441.11196 Math. Nachr. 292, No. 6, 1238-1245 (2019). MSC: 11M06 11M26 PDF BibTeX XML Cite \textit{S. Chaubey} et al., Math. Nachr. 292, No. 6, 1238--1245 (2019; Zbl 1441.11196) Full Text: DOI
Tian, Peng; Qin, Hourong Non-vanishing Fourier coefficients of \(\Delta_k\). (English) Zbl 1428.11081 Appl. Math. Comput. 339, 507-515 (2018). MSC: 11F30 11F33 11F80 PDF BibTeX XML Cite \textit{P. Tian} and \textit{H. Qin}, Appl. Math. Comput. 339, 507--515 (2018; Zbl 1428.11081) Full Text: DOI
Williams, Brandon Rankin-Cohen brackets and Serre derivatives as Poincaré series. (English) Zbl 1444.11061 Res. Number Theory 4, No. 4, Paper No. 37, 13 p. (2018). MSC: 11F11 11F25 PDF BibTeX XML Cite \textit{B. Williams}, Res. Number Theory 4, No. 4, Paper No. 37, 13 p. (2018; Zbl 1444.11061) Full Text: DOI
Barbero, Stefano; Cerruti, Umberto; Murru, Nadir An isomorphism between the convolution product and the componentwise sum connected to the D’Arcais numbers and the Ramanujan tau function. (English) Zbl 1431.11037 Res. Number Theory 4, No. 3, Paper No. 28, 10 p. (2018). MSC: 11B75 11A25 11T06 13F25 PDF BibTeX XML Cite \textit{S. Barbero} et al., Res. Number Theory 4, No. 3, Paper No. 28, 10 p. (2018; Zbl 1431.11037) Full Text: DOI
Cheng, Kaimin A note on the Ramanujan’s tau function. (Chinese. English summary) Zbl 1413.11006 J. Math., Wuhan Univ. 38, No. 2, 337-344 (2018). MSC: 11A25 11A07 PDF BibTeX XML Cite \textit{K. Cheng}, J. Math., Wuhan Univ. 38, No. 2, 337--344 (2018; Zbl 1413.11006) Full Text: DOI
Ramakrishnan, B.; Sahu, Brundaban; Singh, Anup Kumar On the number of representations of certain quadratic forms and a formula for the Ramanujan tau function. (English) Zbl 1418.11057 Funct. Approximatio, Comment. Math. 58, No. 2, 233-244 (2018). MSC: 11E25 11F11 11F30 11E20 PDF BibTeX XML Cite \textit{B. Ramakrishnan} et al., Funct. Approximatio, Comment. Math. 58, No. 2, 233--244 (2018; Zbl 1418.11057) Full Text: DOI Euclid arXiv
Garvan, Frank; Schlosser, Michael J. Combinatorial interpretations of Ramanujan’s tau function. (English) Zbl 1393.05061 Discrete Math. 341, No. 10, 2831-2840 (2018). MSC: 05A30 05A17 11P81 11A07 PDF BibTeX XML Cite \textit{F. Garvan} and \textit{M. J. Schlosser}, Discrete Math. 341, No. 10, 2831--2840 (2018; Zbl 1393.05061) Full Text: DOI
Weba, Michael Finite representations of the summatory divisor function and Ramanujan’s \(\tau\)-function. (English) Zbl 1414.11007 Integers 17, Paper A60, 12 p. (2017). MSC: 11A25 PDF BibTeX XML Cite \textit{M. Weba}, Integers 17, Paper A60, 12 p. (2017; Zbl 1414.11007) Full Text: Link
Hirschhorn, Michael D. Ramanujan’s tau function. (English) Zbl 1433.11040 Andrews, George E. (ed.) et al., Analytic number theory, modular forms and \(q\)-hypergeometric series. In honor of Krishna Alladi’s 60th birthday, University of Florida, Gainesville, FL, USA, March 17–21, 2016. Cham: Springer. Springer Proc. Math. Stat. 221, 311-328 (2017). MSC: 11F11 11F20 11F27 PDF BibTeX XML Cite \textit{M. D. Hirschhorn}, Springer Proc. Math. Stat. 221, 311--328 (2017; Zbl 1433.11040) Full Text: DOI
Sugiyama, Kennichi On a congruence of Fourier coefficients of an eta product. (English) Zbl 1414.11054 Comment. Math. Univ. St. Pauli 66, No. 1-2, 45-61 (2017). MSC: 11F30 11E12 11F33 11F80 14K25 PDF BibTeX XML Cite \textit{K. Sugiyama}, Comment. Math. Univ. St. Pauli 66, No. 1--2, 45--61 (2017; Zbl 1414.11054)
Cheng, Kaimin A new representation of the Ramanujan’s tau function. (Chinese. English summary) Zbl 1389.11003 Pure Appl. Math. 33, No. 2, 129-133 (2017). MSC: 11A25 11A07 PDF BibTeX XML Cite \textit{K. Cheng}, Pure Appl. Math. 33, No. 2, 129--133 (2017; Zbl 1389.11003) Full Text: DOI
Murty, M. Ram; Dewar, Michael; Graves, Hester Problems in the theory of modular forms. (English) Zbl 07312883 HBA Lecture Notes in Mathematics. IMSc Lecture Notes in Mathematics. Cham: Springer; New Delhi: Hindustan Book Agency (ISBN 978-981-10-2651-5/ebook). xvii, 291 p., electronic only. (2016). MSC: 11-02 11F03 11F06 11F20 11F11 00A07 PDF BibTeX XML Cite \textit{M. R. Murty} et al., Problems in the theory of modular forms. Cham: Springer; New Delhi: Hindustan Book Agency (2016; Zbl 07312883) Full Text: DOI
Ramakrishnan, B.; Sahu, Brundaban Identities for the Ramanujan tau function and certain convolution sum identities for the divisor functions. (English) Zbl 1418.11072 Murty, Vijaya Kumar (ed.) et al., Highly composite: papers in number theory. On the occasion of R. Balsubramanian’s 60th birth anniversary. Including papers from the international meeting on number theory, Harish-Chandra Research Institute, Allahabad, India, December 15–20, 2011. Mysore: Ramanujan Mathematical Society. Ramanujan Math. Soc. Lect. Notes Ser. 23, 63-75 (2016). MSC: 11F25 11F11 11A25 PDF BibTeX XML Cite \textit{B. Ramakrishnan} and \textit{B. Sahu}, Ramanujan Math. Soc. Lect. Notes Ser. 23, 63--75 (2016; Zbl 1418.11072)
Bravo, Jhon J.; Luca, Florian Factorials and the Ramanujan function. (English) Zbl 1331.11034 Glasg. Math. J. 58, No. 1, 177-185 (2016). Reviewer: Mehdi Hassani (Zanjan) MSC: 11F30 11D57 PDF BibTeX XML Cite \textit{J. J. Bravo} and \textit{F. Luca}, Glasg. Math. J. 58, No. 1, 177--185 (2016; Zbl 1331.11034) Full Text: DOI
Trudgian, T. S. A short extension of two of Spira’s results. (English) Zbl 1382.11064 J. Math. Inequal. 9, No. 3, 795-798 (2015). MSC: 11M26 11M06 PDF BibTeX XML Cite \textit{T. S. Trudgian}, J. Math. Inequal. 9, No. 3, 795--798 (2015; Zbl 1382.11064) Full Text: DOI
Williams, Kenneth S. Historical remark on Ramanujan’s tau function. (English) Zbl 1336.11037 Am. Math. Mon. 122, No. 1, 30-35 (2015). Reviewer: Jeremy Lovejoy (Paris) MSC: 11F27 11A05 01A60 11F11 11F20 PDF BibTeX XML Cite \textit{K. S. Williams}, Am. Math. Mon. 122, No. 1, 30--35 (2015; Zbl 1336.11037) Full Text: DOI
Murty, M. Ram; Dewar, Michael; Graves, Hester Problems in the theory of modular forms. (English) Zbl 1357.11002 Institute of Mathematical Sciences Lecture Notes 1. New Delhi: Hindustan Book Agency (ISBN 978-93-80250-72-4/pbk; 978-981-10-2651-5/ebook). xv, 291 p. (2015). Reviewer: Yilmaz Simsek (Antalya) MSC: 11-02 11F03 11F06 11F20 11F11 00A07 PDF BibTeX XML Cite \textit{M. R. Murty} et al., Problems in the theory of modular forms. New Delhi: Hindustan Book Agency (2015; Zbl 1357.11002) Full Text: DOI
Dixit, Atul; Roy, Arindam; Zaharescu, Alexandru Ramanujan-Hardy-Littlewood-Riesz phenomena for Hecke forms. (English) Zbl 1383.11064 J. Math. Anal. Appl. 426, No. 1, 594-611 (2015). MSC: 11F60 11M26 PDF BibTeX XML Cite \textit{A. Dixit} et al., J. Math. Anal. Appl. 426, No. 1, 594--611 (2015; Zbl 1383.11064) Full Text: DOI
Tian, Peng Computations of Galois representations associated to modular forms of level one. (English) Zbl 1334.11092 Acta Arith. 164, No. 4, 399-411 (2014). Reviewer: Michael Pohst (Düsseldorf) MSC: 11Y35 11F80 11F03 11-04 PDF BibTeX XML Cite \textit{P. Tian}, Acta Arith. 164, No. 4, 399--411 (2014; Zbl 1334.11092) Full Text: DOI arXiv
Robbins, Neville Inspired by Ramanujan. (English) Zbl 1290.11136 J. Indian Math. Soc., New Ser. 2013, Spec. Issue, 93-96 (2013). MSC: 11P81 11P84 PDF BibTeX XML Cite \textit{N. Robbins}, J. Indian Math. Soc., New Ser. 2013, 93--96 (2013; Zbl 1290.11136)
Rogers, Mathew Identities for the Ramanujan zeta function. (English) Zbl 1285.11068 Adv. Appl. Math. 51, No. 2, 266-275 (2013). Reviewer: Noburo Ishii (Kyoto) MSC: 11F11 11F03 11Y60 33C75 33E05 PDF BibTeX XML Cite \textit{M. Rogers}, Adv. Appl. Math. 51, No. 2, 266--275 (2013; Zbl 1285.11068) Full Text: DOI arXiv
Moriya, B. K.; Smyth, C. J. Index-dependent divisors of coefficients of modular forms. (English) Zbl 1309.11035 Int. J. Number Theory 9, No. 7, 1841-1853 (2013). MSC: 11F20 11F30 11B39 PDF BibTeX XML Cite \textit{B. K. Moriya} and \textit{C. J. Smyth}, Int. J. Number Theory 9, No. 7, 1841--1853 (2013; Zbl 1309.11035) Full Text: DOI
El Gradechi, Amine M. The Lie theory of certain modular form and arithmetic identities. (English) Zbl 1281.11038 Ramanujan J. 31, No. 3, 397-433 (2013). MSC: 11F11 11F22 11F25 11F30 PDF BibTeX XML Cite \textit{A. M. El Gradechi}, Ramanujan J. 31, No. 3, 397--433 (2013; Zbl 1281.11038) Full Text: DOI
Berndt, Bruce C.; Kim, Byungchan; Williams, Kenneth S. Euler products in Ramanujan’s lost notebook. (English) Zbl 1281.11086 Int. J. Number Theory 9, No. 5, 1313-1349 (2013). Reviewer: A. Sankaranarayanan (Mumbai) MSC: 11M41 11F03 11F30 PDF BibTeX XML Cite \textit{B. C. Berndt} et al., Int. J. Number Theory 9, No. 5, 1313--1349 (2013; Zbl 1281.11086) Full Text: DOI
Elliott, P. D. T. A. A central limit theorem for Ramanujan’s tau function. (English) Zbl 1277.11094 Ramanujan J. 29, No. 1-3, 145-161 (2012). Reviewer: Yuk-Kam Lau (Pokfulam) MSC: 11N60 11N36 11N37 11F11 11F30 PDF BibTeX XML Cite \textit{P. D. T. A. Elliott}, Ramanujan J. 29, No. 1--3, 145--161 (2012; Zbl 1277.11094) Full Text: DOI
Kurokawa, Nobushige; Kurihara, Masato; Saito, Takeshi Number theory 3. Iwasawa theory and modular forms. Transl. from the Japanese by Masato Kuwata. (English) Zbl 1259.11001 Translations of Mathematical Monographs 242; Iwanami Series in Modern Mathematics. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-2095-7/pbk). xiv, 226 p. (2012). Reviewer: Franz Lemmermeyer (Jagstzell) MSC: 11-01 11F03 11M36 11R23 11S37 PDF BibTeX XML Cite \textit{N. Kurokawa} et al., Number theory 3. Iwasawa theory and modular forms. Transl. from the Japanese by Masato Kuwata. Providence, RI: American Mathematical Society (AMS) (2012; Zbl 1259.11001)
Murty, M. Ram; Murty, V. Kumar A variant of the Lang-Trotter conjecture. (English) Zbl 1276.11159 Goldfeld, Dorian (ed.) et al., Number theory, analysis and geometry. In memory of Serge Lang. Berlin: Springer (ISBN 978-1-4614-1259-5/hbk; 978-1-4614-1260-1/ebook). 461-474 (2012). MSC: 11N75 11F30 11G05 11R44 PDF BibTeX XML Cite \textit{M. R. Murty} and \textit{V. K. Murty}, in: Number theory, analysis and geometry. In memory of Serge Lang. Berlin: Springer. 461--474 (2012; Zbl 1276.11159) Full Text: DOI
Snurnitsyn, P. V. On basic properties of the Ramanujan \(\tau\)-function. (English. Russian original) Zbl 1301.11048 Math. Notes 90, No. 5, 723-729 (2011); translation from Mat. Zametki 90, No. 5, 736-743 (2011). Reviewer: Tatyana L. Todorova (Sofia) MSC: 11F27 11F11 11L07 11P32 PDF BibTeX XML Cite \textit{P. V. Snurnitsyn}, Math. Notes 90, No. 5, 723--729 (2011; Zbl 1301.11048); translation from Mat. Zametki 90, No. 5, 736--743 (2011) Full Text: DOI
Snurnitsyn, P. V. An additive problem with Ramanujan’s function. (Russian) Zbl 1301.11068 Chebyshevskiĭ Sb. 12, No. 4(40), 112-128 (2011). Reviewer: Tatyana L. Todorova (Sofia) MSC: 11P05 11F27 11P55 PDF BibTeX XML Cite \textit{P. V. Snurnitsyn}, Chebyshevskiĭ Sb. 12, No. 4(40), 112--128 (2011; Zbl 1301.11068) Full Text: MNR
Lygeros, Nik; Rozier, Olivier A new solution to the equation \(\tau(p)\equiv 0\pmod p\). (English) Zbl 1216.11055 J. Integer Seq. 13, No. 7, Article ID 10.7.4, 11 p. (2010). MSC: 11F33 11E41 11R29 11Y35 PDF BibTeX XML Cite \textit{N. Lygeros} and \textit{O. Rozier}, J. Integer Seq. 13, No. 7, Article ID 10.7.4, 11 p. (2010; Zbl 1216.11055) Full Text: EMIS EuDML
Fuselier, Jenny G. Hypergeometric functions over \(\mathbb F_p\) and relations to elliptic curves and modular forms. (English) Zbl 1222.11058 Proc. Am. Math. Soc. 138, No. 1, 109-123 (2010). Reviewer: Florin Nicolae (Berlin) MSC: 11F11 11F25 11G07 11T24 33E50 PDF BibTeX XML Cite \textit{J. G. Fuselier}, Proc. Am. Math. Soc. 138, No. 1, 109--123 (2010; Zbl 1222.11058) Full Text: DOI arXiv
Ernvall-Hytönen, Anne-Maria; Lepistö, Arto Bounds and computational results for exponential sums related to cusp forms. (English) Zbl 1246.11138 Acta Math. Univ. Ostrav. 17, No. 1, 81-90 (2009). Reviewer: Huaning Liu (Shaanxi) MSC: 11L07 11Y35 PDF BibTeX XML Cite \textit{A.-M. Ernvall-Hytönen} and \textit{A. Lepistö}, Acta Math. Univ. Ostrav. 17, No. 1, 81--90 (2009; Zbl 1246.11138) Full Text: Link EuDML
Ono, Ken A mock theta function for the delta-function. (English) Zbl 1230.11056 Landman, Bruce (ed.) et al., Combinatorial number theory. Proceedings of the 3rd ‘Integers Conference 2007’, Carrollton, GA, USA, October 24–27, 2007. Berlin: Walter de Gruyter (ISBN 978-3-11-020221-2/hbk), Integers 9, Suppl., Article A11, 141-155 (2009). Reviewer: Marvin I. Knopp (Philadelphia) MSC: 11F37 11F30 11F33 11F60 PDF BibTeX XML Cite \textit{K. Ono}, in: Combinatorial number theory. Proceedings of the 3rd `Integers Conference 2007', Carrollton, GA, USA, October 24--27, 2007. Berlin: Walter de Gruyter. 141--155 (2009; Zbl 1230.11056) Full Text: DOI
Wage, Matthew On Lehmer-type questions for special classes of arithmetic functions. (English) Zbl 1178.11063 Int. J. Mod. Math. 3, No. 3, 245-260 (2008). Reviewer: Jürgen Spilker (Freiburg i. Br.) MSC: 11N64 11M41 PDF BibTeX XML Cite \textit{M. Wage}, Int. J. Mod. Math. 3, No. 3, 245--260 (2008; Zbl 1178.11063)
Qureshi, M. I.; Khan, Izharul H.; Chaudhary, Wali Mohd. Extended values of Ramanujan’s tau function. (English) Zbl 1171.11310 South East Asian J. Math. Math. Sci. 6, No. 2, 125-129 (2008). MSC: 11F20 11Y70 PDF BibTeX XML Cite \textit{M. I. Qureshi} et al., South East Asian J. Math. Math. Sci. 6, No. 2, 125--129 (2008; Zbl 1171.11310)
Bach, Eric; Charles, Denis The hardness of computing an eigenform. (English) Zbl 1195.11167 Lauter, Kristin E. (ed.) et al., Computational arithmetic geometry. AMS special session, San Francisco, CA, USA, April 29–30, 2006. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4320-8/pbk). Contemporary Mathematics 463, 9-15 (2008). Reviewer: Tom M. Apostol (Pasadena) MSC: 11Y35 11F30 68Q25 68Q17 PDF BibTeX XML Cite \textit{E. Bach} and \textit{D. Charles}, Contemp. Math. 463, 9--15 (2008; Zbl 1195.11167) Full Text: arXiv
Lachterman, Samuel; Schayer, Rhiannon; Younger, Brendan A new proof of the Ramanujan congruences for the partition function. (English) Zbl 1175.11060 Ramanujan J. 15, No. 2, 197-204 (2008). Reviewer: Jeremy Lovejoy (Paris) MSC: 11P83 11F33 PDF BibTeX XML Cite \textit{S. Lachterman} et al., Ramanujan J. 15, No. 2, 197--204 (2008; Zbl 1175.11060) Full Text: DOI
Schwarz, W.; Steuding, R.; Steuding, J. Universality for Euler products, and related arithmetical functions. (English) Zbl 1168.11037 Laurinčikas, A. (ed.) et al., Analytic and probabilistic methods in number theory. Proceedings of the 4th international conference in honour of J. Kubilius, Palanga, Lithuania, September 25–29, 2006. Vilnius: TEV (ISBN 978-9955-680-81-9/hbk). 163-189 (2007). Reviewer: Roma Kačinskaitė (Siauliai) MSC: 11M41 PDF BibTeX XML Cite \textit{W. Schwarz} et al., in: Analytic and probabilistic methods in number theory. Proceedings of the 4th international conference in honour of J. Kubilius, Palanga, Lithuania, September 25--29, 2006. Vilnius: TEV. 163--189 (2007; Zbl 1168.11037)
Garaev, M. Z.; Garcia, V. C.; Konyagin, S. V. A note on the Ramanujan \(\tau\)-function. (English) Zbl 1209.11086 Arch. Math. 89, No. 5, 411-418 (2007). Reviewer: Florian Luca (Morelia) MSC: 11N25 11F30 PDF BibTeX XML Cite \textit{M. Z. Garaev} et al., Arch. Math. 89, No. 5, 411--418 (2007; Zbl 1209.11086) Full Text: DOI
Conrey, J. B.; Snaith, N. C. Applications of the \(L\)-functions ratios conjectures. (English) Zbl 1183.11050 Proc. Lond. Math. Soc. (3) 94, No. 3, 594-646 (2007). Reviewer: Roma Kačinskaitė (Siauliai) MSC: 11M26 11M06 11M50 11M41 22C05 PDF BibTeX XML Cite \textit{J. B. Conrey} and \textit{N. C. Snaith}, Proc. Lond. Math. Soc. (3) 94, No. 3, 594--646 (2007; Zbl 1183.11050) Full Text: DOI arXiv
Charles, Denis Xavier Computing the Ramanujan tau function. (English) Zbl 1109.11066 Ramanujan J. 11, No. 2, 221-224 (2006). Reviewer: Tom M. Apostol (Pasadena) MSC: 11Y55 11F11 11-04 PDF BibTeX XML Cite \textit{D. X. Charles}, Ramanujan J. 11, No. 2, 221--224 (2006; Zbl 1109.11066) Full Text: DOI
Luca, Florian; Shparlinski, Igor E. Arithmetic properties of the Ramanujan function. (English) Zbl 1095.11044 Proc. Indian Acad. Sci., Math. Sci. 116, No. 1, 1-8 (2006). Reviewer: Eira J. Scourfield (Egham) MSC: 11N56 PDF BibTeX XML Cite \textit{F. Luca} and \textit{I. E. Shparlinski}, Proc. Indian Acad. Sci., Math. Sci. 116, No. 1, 1--8 (2006; Zbl 1095.11044) Full Text: DOI arXiv
Alkan, Emre; Zaharescu, Alexandru; Zaki, Mohammad Arithmetical functions in several variables. (English) Zbl 1088.11005 Int. J. Number Theory 1, No. 3, 383-399 (2005). Reviewer: Władysław Narkiewicz (Wrocław) MSC: 11A25 13F30 13J10 PDF BibTeX XML Cite \textit{E. Alkan} et al., Int. J. Number Theory 1, No. 3, 383--399 (2005; Zbl 1088.11005) Full Text: DOI
Shparlinski, Igor E. On the value set of the Ramanujan function. (English) Zbl 1115.11013 Arch. Math. 85, No. 6, 508-513 (2005). Reviewer: Luis Gallardo (Brest) MSC: 11B50 11F11 11T23 PDF BibTeX XML Cite \textit{I. E. Shparlinski}, Arch. Math. 85, No. 6, 508--513 (2005; Zbl 1115.11013) Full Text: DOI
Alkan, Emre; Zaharescu, Alexandru Nonvanishing of the Ramanujan tau function in short intervals. (English) Zbl 1075.11035 Int. J. Number Theory 1, No. 1, 45-51 (2005). Reviewer: Florin Nicolae (Berlin) MSC: 11F30 11H99 PDF BibTeX XML Cite \textit{E. Alkan} and \textit{A. Zaharescu}, Int. J. Number Theory 1, No. 1, 45--51 (2005; Zbl 1075.11035) Full Text: DOI
Moree, Pieter On some claims in Ramanujan’s ‘unpublished’ manuscript on the partition and tau functions. (English) Zbl 1066.11059 Ramanujan J. 8, No. 3, 317-330 (2004). Reviewer: Ekkehard Krätzel (Jena) MSC: 11Y60 11N37 PDF BibTeX XML Cite \textit{P. Moree}, Ramanujan J. 8, No. 3, 317--330 (2004; Zbl 1066.11059) Full Text: DOI arXiv
Lanphier, Dominic Maass operators and van der Pol-type identities for Ramanujan’s tau function. (English) Zbl 1114.11043 Acta Arith. 113, No. 2, 157-167 (2004). Reviewer: Jeremy Lovejoy (Paris) MSC: 11F30 11F25 11F37 PDF BibTeX XML Cite \textit{D. Lanphier}, Acta Arith. 113, No. 2, 157--167 (2004; Zbl 1114.11043) Full Text: DOI Link
Liu, Zhi-Guo An identity of Ramanujan and the representation of integers as sums of triangular numbers. (English) Zbl 1041.11028 Ramanujan J. 7, No. 4, 407-434 (2003). MSC: 11F11 11F12 11F27 33E05 11E25 PDF BibTeX XML Cite \textit{Z.-G. Liu}, Ramanujan J. 7, No. 4, 407--434 (2003; Zbl 1041.11028) Full Text: DOI
Friedberg, Solomon A note on base change, identities involving \({\tau}(n)\), and a congruence of Ramanujan. (English) Zbl 1040.11031 Ramanujan J. 7, No. 1-3, 165-168 (2003). Reviewer: Tom M. Apostol (Pasadena) MSC: 11F30 PDF BibTeX XML Cite \textit{S. Friedberg}, Ramanujan J. 7, No. 1--3, 165--168 (2003; Zbl 1040.11031) Full Text: DOI
Berndt, Bruce C.; Kohnen, Winfried; Ono, Ken The life and work of R. A. Rankin (1915–2001). (English) Zbl 1039.01011 Ramanujan J. 7, No. 1-3, 9-38 (2003). MSC: 01A70 11-03 PDF BibTeX XML Cite \textit{B. C. Berndt} et al., Ramanujan J. 7, No. 1--3, 9--38 (2003; Zbl 1039.01011) Full Text: DOI
Hafner, James Lee; Stopple, Jeffrey A heat kernel associated to Ramanujan’s tau function. (English) Zbl 0987.11055 Ramanujan J. 4, No. 2, 123-128 (2000). Reviewer: Matti Jutila (Turku) MSC: 11M36 11F72 11M26 11N37 11F30 PDF BibTeX XML Cite \textit{J. L. Hafner} and \textit{J. Stopple}, Ramanujan J. 4, No. 2, 123--128 (2000; Zbl 0987.11055) Full Text: DOI
Hirschhorn, Michael D. An identity of Ramanujan, and applications. (English) Zbl 0964.11045 Ismail, Mourad E. H. (ed.) et al., \(q\)-series from a contemporary perspective. AMS-IMS-SIAM joint summer research conference on \(q\)-series, combinatorics, and computer algebra, South Hadley, MA, USA, June 21-25, 1998. Providence, RI: American Mathematical Society. Contemp. Math. 254, 229-234 (2000). Reviewer: Shaun Cooper (Auckland) MSC: 11P83 11F03 11F20 PDF BibTeX XML Cite \textit{M. D. Hirschhorn}, Contemp. Math. 254, 229--234 (2000; Zbl 0964.11045)
Ewell, John A. New representations of Ramanujan’s tau function. (English) Zbl 0966.11003 Proc. Am. Math. Soc. 128, No. 3, 723-726 (2000). Reviewer: Tom M.Apostol (Pasadena) MSC: 11A25 05A19 PDF BibTeX XML Cite \textit{J. A. Ewell}, Proc. Am. Math. Soc. 128, No. 3, 723--726 (2000; Zbl 0966.11003) Full Text: DOI
Berndt, Bruce C.; Ono, Ken Ramanujan’s unpublished manuscript on the partition and tau functions with proofs and commentary. (English) Zbl 0932.11002 Sémin. Lothar. Comb. 42, B42c, 63 p. (1999). Reviewer: M.Sheingorn (New York) MSC: 11-03 01A60 11-02 11P83 11P82 11F11 PDF BibTeX XML Cite \textit{B. C. Berndt} and \textit{K. Ono}, Sémin. Lothar. Comb. 42, B42c, 63 p. (1999; Zbl 0932.11002) Full Text: EMIS EuDML
Kim, Daeyeoul; Park, Joongsoo A study of Ramanujan \(\tau(n)\) number and Dedekind eta-function. (English) Zbl 0978.11017 Honam Math. J. 20, No. 1, 57-65 (1998). Reviewer: Tom M.Apostol (Pasadena) MSC: 11F20 11F27 PDF BibTeX XML Cite \textit{D. Kim} and \textit{J. Park}, Honam Math. J. 20, No. 1, 57--65 (1998; Zbl 0978.11017)
Ewell, J. A. On Ramanujan’s tau function. (English) Zbl 0942.11007 Rocky Mt. J. Math. 28, No. 2, 453-461 (1998). Reviewer: Jürgen Spilker (Freiburg im Breisgau) MSC: 11A25 11B75 PDF BibTeX XML Cite \textit{J. A. Ewell}, Rocky Mt. J. Math. 28, No. 2, 453--461 (1998; Zbl 0942.11007) Full Text: DOI Link
Elliott, P. D. T. A. Duality in analytic number theory. (English) Zbl 0887.11002 Cambridge Tracts in Mathematics. 122. Cambridge: Cambridge University Press. xviii, 341 p. (1997). Reviewer: Wolfgang Schwarz (Frankfurt am Main) MSC: 11-02 11K65 11N37 11N60 11N64 PDF BibTeX XML Cite \textit{P. D. T. A. Elliott}, Duality in analytic number theory. Cambridge: Cambridge University Press (1997; Zbl 0887.11002)
Vorhauer, Ulrike Magdalena Anna Estimation of the error term for Riesz means of Dirichlet series with functional equation. (Restgliedabschätzung bei Riesz-Mitteln von Dirichlet-Reihen mit Funktionalgleichungen.) (German) Zbl 0862.11053 Ulm: Univ. Ulm, Fak. Math. und Wirtschaftswiss. 280 S. (1995). Reviewer: D.Wolke (Freiburg i.Br.) MSC: 11N37 11L07 11L40 11F20 PDF BibTeX XML Cite \textit{U. M. A. Vorhauer}, Restgliedabschätzung bei Riesz-Mitteln von Dirichlet-Reihen mit Funktionalgleichungen. Ulm: Univ. Ulm, Fak. Math. und Wirtschaftswiss. (1995; Zbl 0862.11053)
Deutsch, Jesse Ira Conjectures relating to a generalization of the Ramanujan tau function. (English) Zbl 0751.11027 Number theory, Proc. Semin., New York/NY (USA) 1989-1990, 105-118 (1991). Reviewer: J.L.Hafner (San José) MSC: 11F41 11F60 11F30 11F33 PDF BibTeX XML
Andrianov, A. N. Integration of modular forms with theta-series. (Russian) Zbl 0736.11026 Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 183, 5-21 (1990). Reviewer: M.Peters (Münster) MSC: 11F66 11F27 11F11 PDF BibTeX XML Cite \textit{A. N. Andrianov}, Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 183, 5--21 (1990; Zbl 0736.11026) Full Text: EuDML
Newman, Morris Some powers of the Euler product. (English) Zbl 0724.11025 Analytic number theory, Proc. Conf. in Honor of Paul T. Bateman, Urbana/IL (USA) 1989, Prog. Math. 85, 405-411 (1990). Reviewer: G.Köhler (Würzburg) MSC: 11F20 11F30 PDF BibTeX XML
Andrianov, A. N. Integration of modular forms with theta series. (English. Russian original) Zbl 0784.11021 J. Sov. Math. 62, No. 4, 2833-2844 (1992); translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 183, 5-21 (1990). MSC: 11F66 11F27 11F11 PDF BibTeX XML Cite \textit{A. N. Andrianov}, J. Sov. Math. 62, No. 4, 5--21 (1990; Zbl 0784.11021); translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 183, 5--21 (1990) Full Text: DOI
Mauclaire, Jean-Loup Deux résultats de théorie probabiliste des nombres. (Two results in probabilistic number theory). (French) Zbl 0766.11036 C. R. Acad. Sci., Paris, Sér. I 311, No. 2, 69-72 (1990). Reviewer: I.Z.Ruzsa (Budapest) MSC: 11K99 11K65 11N45 11N80 PDF BibTeX XML Cite \textit{J.-L. Mauclaire}, C. R. Acad. Sci., Paris, Sér. I 311, No. 2, 69--72 (1990; Zbl 0766.11036)
Sivaramakrishnan, R. Classical theory of arithmetic functions. (English) Zbl 0657.10001 Pure and Applied Mathematics, 126. New York, NY etc.: Marcel Dekker, Inc. xii, 386 p. $ 99.75/US and Canada; $ 119.50/outside (1989). Reviewer: W.Narkiewicz MSC: 11-02 11A25 PDF BibTeX XML Cite \textit{R. Sivaramakrishnan}, Classical theory of arithmetic functions. New York, NY etc.: Marcel Dekker, Inc. (1989; Zbl 0657.10001)
Shorey, T. N. Some exponential diophantine equations. II. (English) Zbl 0748.11022 Number theory and related topics, Pap. Ramanujan Colloq., Bombay/India 1988, Stud. Math., Tata Inst. Fundam. Res. 12, 217-229 (1989). Reviewer: R.J.Stroeker (Rotterdam) MSC: 11D61 11B37 PDF BibTeX XML Cite \textit{T. N. Shorey}, in: Number theory and related topics. Papers presented at the Ramanujan birth centenary international colloquium, Bombay, India, 4-11 January, 1988. Oxford: Oxford University Press, published for the Tata Institute of Fundamental Research. 217--229 (1989; Zbl 0748.11022)
Swinnerton-Dyer, H. P. F. Congruence properties of \(\tau\) (n). (English) Zbl 0655.10028 Ramanujan revisited, Proc. Conf., Urbana-Champaign/Illinois 1987, 289-311 (1988). Reviewer: J.L.Hafner MSC: 11F33 11F11 11F80 PDF BibTeX XML
Conrey, J. B.; Ghosh, A. Simple zeros of the Ramanujan \(\tau\)-Dirichlet series. (English) Zbl 0653.10038 Invent. Math. 94, No. 2, 403-419 (1988). Reviewer: B.Z.Moroz MSC: 11M35 11F67 PDF BibTeX XML Cite \textit{J. B. Conrey} and \textit{A. Ghosh}, Invent. Math. 94, No. 2, 403--419 (1988; Zbl 0653.10038) Full Text: DOI EuDML
Conrey, J. B.; Ghosh, A. Simple zeros of the Dirichlet series formed with Ramanujan’s tau- functions. (English) Zbl 0652.10030 C. R. Math. Acad. Sci., Soc. R. Can. 10, No. 2, 95-99 (1988). Reviewer: B.Z.Moroz MSC: 11M35 11F67 PDF BibTeX XML Cite \textit{J. B. Conrey} and \textit{A. Ghosh}, C. R. Math. Acad. Sci., Soc. R. Can. 10, No. 2, 95--99 (1988; Zbl 0652.10030)
Murty, M. Ram The Ramanujan \(\tau\) function. (English) Zbl 0645.10025 Ramanujan revisited, Proc. Conf., Urbana-Champaign/Illinois 1987, 269-288 (1988). Reviewer: James L. Hafner (San José) MSC: 11F11 PDF BibTeX XML
Rankin, R. A. Ramanujan’s tau-function and its generalizations. (English) Zbl 0645.10024 Ramanujan revisited, Proc. Conf., Urbana-Champaign/Illinois 1987, 245-268 (1988). Reviewer: James L. Hafner (San José) MSC: 11F11 11F33 11F67 11-02 PDF BibTeX XML
Shorey, T. N. Ramanujan and binary recursive sequences. (English) Zbl 0669.10020 J. Indian Math. Soc., New Ser. 52, 147-157 (1987). Reviewer: R.J.Stroeker MSC: 11B37 11J81 11F11 PDF BibTeX XML Cite \textit{T. N. Shorey}, J. Indian Math. Soc., New Ser. 52, 147--157 (1987; Zbl 0669.10020)
Ramachandra, K. Srinivasa Ramanujan. (The inventor of the circle method). (22.12.1887 to 26.4.1920). Inaugural address. (English) Zbl 0669.10002 Hardy-Ramanujan J. 10, 9-24 (1987). Reviewer: J.Brüdern MSC: 11-03 01A60 11P81 11P05 11P32 11P55 PDF BibTeX XML Cite \textit{K. Ramachandra}, Hardy-Ramanujan J. 10, 9--24 (1987; Zbl 0669.10002)
Jutila, M. On exponential sums involving the Ramanujan function. (English) Zbl 0658.10043 Proc. Indian Acad. Sci., Math. Sci. (Ramanujan Birth Centenary Volume) 97, No. 1-3, 157-166 (1987). Reviewer: M.Sheingorn MSC: 11L40 11F11 PDF BibTeX XML Cite \textit{M. Jutila}, Proc. Indian Acad. Sci., Math. Sci. 97, No. 1--3, 157--166 (1987; Zbl 0658.10043) Full Text: DOI
Ramachandra, K. Srinivasa Ramanujan (The inventor of the circle method) (22.12.1887 to 26.4.1920). (English) Zbl 0643.10003 J. Math. Phys. Sci. 21, 545-565 (1987). Reviewer: G.L.Alexanderson MSC: 11-03 01A70 11P55 11P32 11P81 11P05 PDF BibTeX XML Cite \textit{K. Ramachandra}, J. Math. Phys. Sci. 21, 545--565 (1987; Zbl 0643.10003)
Murty, M. Ram; Murty, V. Kumar; Shorey, T. N. Odd values of the Ramanjuan \(\tau\)-function. (English) Zbl 0635.10020 Bull. Soc. Math. Fr. 115, 391-395 (1987). Reviewer: James L. Hafner (San José) MSC: 11F30 11F11 11J68 11D41 11N37 PDF BibTeX XML Cite \textit{M. R. Murty} et al., Bull. Soc. Math. Fr. 115, 391--395 (1987; Zbl 0635.10020) Full Text: DOI Numdam EuDML
Ehrkomaishvili, G. L. On a diophantine equation and its application. (Russian. English summary) Zbl 0648.10014 Tr. Tbilis. Univ. 264, Mat. Mekh. Astron. 21, 21-30 (1986). Reviewer: Li Delang MSC: 11E12 11F11 11E45 PDF BibTeX XML
Purtseladze, A. L. On the Fourier coefficients of the functions \(\Delta\) (\(\tau\) ) and \(\sqrt{\Delta (\tau)}\). (Russian. English summary) Zbl 0643.10017 Tr. Tbilis. Univ. 264, Mat. Mekh. Astron. 21, 5-20 (1986). Reviewer: M.Peters MSC: 11E45 11F11 PDF BibTeX XML
Rankin, R. A. Fourier coefficients of cusp forms. (English) Zbl 0616.10020 Math. Proc. Camb. Philos. Soc. 100, 5-29 (1986). Reviewer: K.Katayama MSC: 11F11 11-02 PDF BibTeX XML Cite \textit{R. A. Rankin}, Math. Proc. Camb. Philos. Soc. 100, 5--29 (1986; Zbl 0616.10020) Full Text: DOI
Shorey, T. N.; Tijdeman, R. Exponential Diophantine equations. (English) Zbl 0606.10011 Cambridge Tracts in Mathematics, 87. Cambridge etc.: Cambridge University Press. x, 240 p. £25.00; $ 44.50 (1986). Reviewer: Bernd Richter (Berlin) MSC: 11D61 11D41 11-02 11D88 11R58 PDF BibTeX XML
Good, A. Dirichlet and Poincaré series. (English) Zbl 0588.10023 Glasg. Math. J. 27, 39-56 (1985). Reviewer: N.V.Kuznetsov MSC: 11F11 11F67 PDF BibTeX XML Cite \textit{A. Good}, Glasg. Math. J. 27, 39--56 (1985; Zbl 0588.10023) Full Text: DOI
Kuznetsov, N. V. Poincaré series and an extension of the Lehmer conjecture. (English. Russian original) Zbl 0588.10022 Russ. Math. Surv. 40, No. 4, 203-204 (1985); translation from Usp. Mat. Nauk 40, No. 4 (244), 181-182 (1985). Reviewer: R.W.Bruggeman MSC: 11F11 PDF BibTeX XML Cite \textit{N. V. Kuznetsov}, Russ. Math. Surv. 40, No. 4, 203--204 (1985; Zbl 0588.10022); translation from Usp. Mat. Nauk 40, No. 4 (244), 181--182 (1985) Full Text: DOI
Ewell, John A. On a function related to Ramanujan’s tau function. (English) Zbl 0583.10003 Int. J. Math. Math. Sci. 8, 795-797 (1985). Reviewer: T.M.Apostol MSC: 11A25 11F03 PDF BibTeX XML Cite \textit{J. A. Ewell}, Int. J. Math. Math. Sci. 8, 795--797 (1985; Zbl 0583.10003) Full Text: DOI EuDML
Purtseladze, A. L. On two formulas of B. Schoeneberg. (Russian) Zbl 0609.10014 Tr. Tbilis. Univ. 252, Mat. Mekh. Astron. 16/17, 34-52 (1984). Reviewer: M.Peters MSC: 11E45 11F11 11F27 PDF BibTeX XML
Perelli, A. On some exponential sums connected with Ramanujan’s \(\tau\) -function. (English) Zbl 0549.10033 Mathematika 31, 150-158 (1984). Reviewer: M.Sheingorn MSC: 11N37 11L40 11F67 11M35 11P55 PDF BibTeX XML Cite \textit{A. Perelli}, Mathematika 31, 150--158 (1984; Zbl 0549.10033) Full Text: DOI
Meier, Holger; Rosenberger, Gerhard Hecke-Integrale mit rationalen periodischen Funktionen und Dirichlet-Reihen mit Funktionalgleichung. (German) Zbl 0542.10016 Result. Math. 7, 209-233 (1984). MSC: 11F67 11F66 PDF BibTeX XML Cite \textit{H. Meier} and \textit{G. Rosenberger}, Result. Math. 7, 209--233 (1984; Zbl 0542.10016) Full Text: DOI
Ewell, John A. A formula for Ramanujan’s tau function. (English) Zbl 0541.10027 Proc. Am. Math. Soc. 91, 37-40 (1984). Reviewer: T.M.Apostol MSC: 11F11 PDF BibTeX XML Cite \textit{J. A. Ewell}, Proc. Am. Math. Soc. 91, 37--40 (1984; Zbl 0541.10027) Full Text: DOI
Murty, M. Ram; Murty, V. Kumar Prime divisors of Fourier coefficients of modular forms. (English) Zbl 0537.10026 Duke Math. J. 51, 57-76 (1984). Reviewer: T. M. Apostol MSC: 11F30 11F11 PDF BibTeX XML Cite \textit{M. R. Murty} and \textit{V. K. Murty}, Duke Math. J. 51, 57--76 (1984; Zbl 0537.10026) Full Text: DOI
Jutila, Matti Transformation formulae for Dirichlet polynomials. (English) Zbl 0533.10034 J. Number Theory 18, 135-156 (1984). Reviewer: H.Müller MSC: 11M06 11F67 PDF BibTeX XML Cite \textit{M. Jutila}, J. Number Theory 18, 135--156 (1984; Zbl 0533.10034) Full Text: DOI
Grupp, F. Eine Bemerkung zur Ramanujan’schen \(\tau\)-Funktion. (German) Zbl 0531.10029 Arch. Math. 43, 358-363 (1984). MSC: 11F11 11N37 PDF BibTeX XML Cite \textit{F. Grupp}, Arch. Math. 43, 358--363 (1984; Zbl 0531.10029) Full Text: DOI
Moreno, Carlos J.; Shahidi, Freydoon The fourth moment of the Ramanujan tau-function. (English) Zbl 0508.10014 Math. Ann. 266, 233-239 (1983). MSC: 11F11 11N37 PDF BibTeX XML Cite \textit{C. J. Moreno} and \textit{F. Shahidi}, Math. Ann. 266, 233--239 (1983; Zbl 0508.10014) Full Text: DOI EuDML
Rankin, R. A. Sums of powers of cusp form coefficients. (English) Zbl 0492.10020 Math. Ann. 263, 227-236 (1983). MSC: 11F11 11N37 PDF BibTeX XML Cite \textit{R. A. Rankin}, Math. Ann. 263, 227--236 (1983; Zbl 0492.10020) Full Text: DOI EuDML
Balasubramanian, R.; Murty, M. Ram An Omega-theorem for Ramanujan’s tau-function. (English) Zbl 0499.10024 Invent. Math. 68, 241-252 (1982). MSC: 11F11 11N37 PDF BibTeX XML Cite \textit{R. Balasubramanian} and \textit{M. R. Murty}, Invent. Math. 68, 241--252 (1982; Zbl 0499.10024) Full Text: DOI
Murty, M. Ram Some Omega-results for Ramanujan’s tau-function. (English) Zbl 0486.10030 Number theory, Proc. 3rd Matsci. Conf., Mysore/India 1981, Lect. Notes Math. 938, 123-137 (1982). MSC: 11N37 11F03 PDF BibTeX XML
Kuznetsov, N. V. Lehmer’s conjecture. I. (English) Zbl 0466.10013 J. Sov. Math. 17, 2116-2137 (1981). MSC: 11F11 11F03 PDF BibTeX XML Cite \textit{N. V. Kuznetsov}, J. Sov. Math. 17, 2116--2137 (1981; Zbl 0466.10013) Full Text: DOI
Bambah, R. P. Srinivasa Ramanujan medal lecture - 1979: Number theory - many challenges, some achievements. (English) Zbl 0535.10002 Proc. Indian Natl. Sci. Acad., Part A 46, 109-118 (1980). Reviewer: T.Vepkhvadze MSC: 11-02 11F11 11H31 11P32 11P05 PDF BibTeX XML Cite \textit{R. P. Bambah}, Proc. Indian Natl. Sci. Acad., Part A 46, 109--118 (1980; Zbl 0535.10002)
Elliott, P. D. T. A. Mean value theorems for multiplicative functions bounded in mean \(\alpha\)-power, \(\alpha >1\). (English) Zbl 0426.10050 J. Aust. Math. Soc., Ser. A 29, 177-205 (1980). MSC: 11N37 11K65 PDF BibTeX XML Cite \textit{P. D. T. A. Elliott}, J. Aust. Math. Soc., Ser. A 29, 177--205 (1980; Zbl 0426.10050)
Doi, K.; Miyake, T. Automorphic forms and number theory. (Japanese) Zbl 0466.10012 Tokyo: Kinokuniya. IX, 373 p. (1976). MSC: 11Fxx 11-01 11F03 11F67 PDF BibTeX XML