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Bhargava, Manjul

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Author ID: bhargava.manjul Recent zbMATH articles by "Bhargava, Manjul"
Published as: Bhargava, Manjul; Bhargava, M.
Homepage: https://www.math.princeton.edu/directory/manjul-bhargava
External Links: MGP · Wikidata · dblp · GND · IdRef
Awards: Clay Research Award (2005) · Fields Medal (2014)
Documents Indexed: 48 Publications since 1997, including 2 Books
Biographic References: 7 Publications

Publications by Year

Citations contained in zbMATH Open

43 Publications have been cited 688 times in 367 Documents Cited by Year
The density of discriminants of quartic rings and fields. Zbl 1159.11045
Bhargava, Manjul
66
2005
\(P\)-orderings and polynomial functions on arbitrary subsets of Dedekind rings. Zbl 0899.13022
Bhargava, Manjul
56
1997
The density of discriminants of quintic rings and fields. Zbl 1220.11139
Bhargava, Manjul
44
2010
The factorial function and generalizations. Zbl 0987.05003
Bhargava, Manjul
42
2000
On the Conway-Schneeberger Fifteen Theorem. Zbl 0987.11027
Bhargava, Manjul
40
2000
Binary quartic forms having bounded invariants, and the boundedness of the average rank of elliptic curves. Zbl 1307.11071
Bhargava, Manjul; Shankar, Arul
35
2015
Higher composition laws. III: The parametrization of quartic rings. Zbl 1169.11045
Bhargava, Manjul
31
2004
Higher composition laws. I: A new view on Gauss composition, and quadratic generalizations. Zbl 1072.11078
Bhargava, Manjul
29
2004
On the Davenport-Heilbronn theorems and second order terms. Zbl 1294.11191
Bhargava, Manjul; Shankar, Arul; Tsimerman, Jacob
29
2013
Mass formulae for extensions of local fields, and conjectures on the density of number field discriminants. Zbl 1145.11080
Bhargava, Manjul
24
2007
Higher composition laws. II: On cubic analogues of Gauss composition. Zbl 1169.11044
Bhargava, Manjul
22
2004
Generalized factorials and fixed divisors over subsets of a Dedekind domain. Zbl 0931.13004
Bhargava, Manjul
21
1998
Higher composition laws. IV: The parametrization of quintic rings. Zbl 1173.11058
Bhargava, Manjul
15
2008
On \(P\)-orderings, rings of integer-valued polynomials, and ultrametric analysis. Zbl 1219.11047
Bhargava, Manjul
15
2009
Error estimates for the Davenport-Heilbronn theorems. Zbl 1227.11114
Belabas, Karim; Bhargava, Manjul; Pomerance, Carl
15
2010
Factoring Dickson polynomials over finite fields. Zbl 0929.11060
Bhargava, Manjul; Zieve, Michael E.
14
1999
The average size of the 2-Selmer group of Jacobians of hyperelliptic curves having a rational Weierstrass point. Zbl 1303.11072
Bhargava, Manjul; Gross, Benedict H.
14
2013
Ternary cubic forms having bounded invariants, and the existence of a positive proportion of elliptic curves having rank 0. Zbl 1317.11038
Bhargava, Manjul; Shankar, Arul
14
2015
Modeling the distribution of ranks, Selmer groups, and Shafarevich-Tate groups of elliptic curves. Zbl 1329.14071
Bhargava, Manjul; Kane, Daniel M.; Lenstra, Hendrik W. jun.; Poonen, Bjorn; Rains, Eric
13
2015
Coregular spaces and genus one curves. Zbl 1342.14074
Bhargava, Manjul; Ho, Wei
12
2016
Arithmetic invariant theory. Zbl 1377.11045
Bhargava, Manjul; Gross, Benedict H.
12
2014
Higher composition laws and applications. Zbl 1129.11049
Bhargava, Manjul
10
2006
The density of discriminants of \(S_3\)-sextic number fields. Zbl 1171.11058
Bhargava, Manjul; Wood, Melanie Matchett
10
2008
The equidistribution of lattice shapes of rings of integers in cubic, quartic, and quintic number fields. Zbl 1347.11074
Bhargava, Manjul; Harron, Piper
10
2016
Continuous functions on compact subsets of local fields. Zbl 0979.11054
Bhargava, Manjul; Kedlaya, Kiran S.
9
1999
A positive proportion of locally soluble hyperelliptic curves over \(\mathbb {Q}\) have no point over any odd degree extension. Zbl 1385.11043
Bhargava, Manjul; Gross, Benedict H.; Wang, Xiaoheng
9
2017
Finite generation properties for various rings of integer-valued polynomials. Zbl 1177.13051
Bhargava, Manjul; Cahen, Paul-Jean; Yeramian, Julie
8
2009
On the number of cubic orders of bounded discriminant having automorphism group \(C_3\), and related problems. Zbl 1298.11102
Bhargava, Manjul; Shnidman, Ariel
8
2014
The proportion of plane cubic curves over \(\mathbb{Q}\) that everywhere locally have a point. Zbl 1341.11033
Bhargava, Manjul; Cremona, John; Fisher, Tom
7
2016
Arithmetic invariant theory II: pure inner forms and obstructions to the existence of orbits. Zbl 1377.11046
Bhargava, Manjul; Gross, Benedict H.; Wang, Xiaoheng
7
2015
On a notion of “Galois closure” for extensions of rings. Zbl 1396.13007
Bhargava, Manjul; Satriano, Matthew
6
2014
The mean number of 3-torsion elements in the class groups and ideal groups of quadratic orders. Zbl 1407.11126
Bhargava, Manjul; Varma, Ila
6
2016
What is the probability that a random integral quadratic form in \(n\) variables has an integral zero? Zbl 1404.11035
Bhargava, Manjul; Cremona, John E.; Fisher, Tom; Jones, Nick G.; Keating, Jonathan P.
6
2016
Bounds on 2-torsion in class groups of number fields and integral points on elliptic curves. Zbl 1456.11101
Bhargava, M.; Shankar, A.; Taniguchi, T.; Thorne, F.; Tsimerman, J.; Zhao, Y.
6
2020
On the mean number of 2-torsion elements in the class groups, narrow class groups, and ideal groups of cubic orders and fields. Zbl 1335.11093
Bhargava, Manjul; Varma, Ila
4
2015
Congruence preservation and polynomial functions from \(\mathbb{Z}_n\) to \(\mathbb{Z}_m\). Zbl 0883.11011
Bhargava, Manjul
3
1997
On the average number of octahedral newforms of prime level. Zbl 1206.11049
Bhargava, Manjul; Ghate, Eknath
3
2009
A positive proportion of elliptic curves over \(\mathbb Q\) have rank one. Zbl 1315.11045
Bhargava, Manjul; Skinner, Christopher
3
2014
Finite simple groups: thirty years of the atlas and beyond. International conference celebrating the atlases and honoring John Conway, Princeton University, Princeton, NJ, USA, November 2–5, 2015. Zbl 1372.20002
Bhargava, Manjul (ed.); Guralnick, Robert (ed.); Hiss, Gerhard (ed.); Lux, Klaus (ed.); Tiep, Pham Huu (ed.)
3
2017
Gauss composition and generalizations. Zbl 1058.11030
Bhargava, Manjul
2
2002
Orbit parametrizations for \(K3\) surfaces. Zbl 1346.14099
Bhargava, Manjul; Ho, Wei; Kumar, Abhinav
2
2016
A positive proportion of Thue equations fail the integral Hasse principle. Zbl 1450.11026
Akhtari, Shabnam; Bhargava, Manjul
2
2019
Rational points on elliptic and hyperelliptic curves. Zbl 1373.11045
Bhargava, Manjul
1
2014
Bounds on 2-torsion in class groups of number fields and integral points on elliptic curves. Zbl 1456.11101
Bhargava, M.; Shankar, A.; Taniguchi, T.; Thorne, F.; Tsimerman, J.; Zhao, Y.
6
2020
A positive proportion of Thue equations fail the integral Hasse principle. Zbl 1450.11026
Akhtari, Shabnam; Bhargava, Manjul
2
2019
A positive proportion of locally soluble hyperelliptic curves over \(\mathbb {Q}\) have no point over any odd degree extension. Zbl 1385.11043
Bhargava, Manjul; Gross, Benedict H.; Wang, Xiaoheng
9
2017
Finite simple groups: thirty years of the atlas and beyond. International conference celebrating the atlases and honoring John Conway, Princeton University, Princeton, NJ, USA, November 2–5, 2015. Zbl 1372.20002
Bhargava, Manjul; Guralnick, Robert; Hiss, Gerhard; Lux, Klaus; Tiep, Pham Huu
3
2017
Coregular spaces and genus one curves. Zbl 1342.14074
Bhargava, Manjul; Ho, Wei
12
2016
The equidistribution of lattice shapes of rings of integers in cubic, quartic, and quintic number fields. Zbl 1347.11074
Bhargava, Manjul; Harron, Piper
10
2016
The proportion of plane cubic curves over \(\mathbb{Q}\) that everywhere locally have a point. Zbl 1341.11033
Bhargava, Manjul; Cremona, John; Fisher, Tom
7
2016
The mean number of 3-torsion elements in the class groups and ideal groups of quadratic orders. Zbl 1407.11126
Bhargava, Manjul; Varma, Ila
6
2016
What is the probability that a random integral quadratic form in \(n\) variables has an integral zero? Zbl 1404.11035
Bhargava, Manjul; Cremona, John E.; Fisher, Tom; Jones, Nick G.; Keating, Jonathan P.
6
2016
Orbit parametrizations for \(K3\) surfaces. Zbl 1346.14099
Bhargava, Manjul; Ho, Wei; Kumar, Abhinav
2
2016
Binary quartic forms having bounded invariants, and the boundedness of the average rank of elliptic curves. Zbl 1307.11071
Bhargava, Manjul; Shankar, Arul
35
2015
Ternary cubic forms having bounded invariants, and the existence of a positive proportion of elliptic curves having rank 0. Zbl 1317.11038
Bhargava, Manjul; Shankar, Arul
14
2015
Modeling the distribution of ranks, Selmer groups, and Shafarevich-Tate groups of elliptic curves. Zbl 1329.14071
Bhargava, Manjul; Kane, Daniel M.; Lenstra, Hendrik W. jun.; Poonen, Bjorn; Rains, Eric
13
2015
Arithmetic invariant theory II: pure inner forms and obstructions to the existence of orbits. Zbl 1377.11046
Bhargava, Manjul; Gross, Benedict H.; Wang, Xiaoheng
7
2015
On the mean number of 2-torsion elements in the class groups, narrow class groups, and ideal groups of cubic orders and fields. Zbl 1335.11093
Bhargava, Manjul; Varma, Ila
4
2015
Arithmetic invariant theory. Zbl 1377.11045
Bhargava, Manjul; Gross, Benedict H.
12
2014
On the number of cubic orders of bounded discriminant having automorphism group \(C_3\), and related problems. Zbl 1298.11102
Bhargava, Manjul; Shnidman, Ariel
8
2014
On a notion of “Galois closure” for extensions of rings. Zbl 1396.13007
Bhargava, Manjul; Satriano, Matthew
6
2014
A positive proportion of elliptic curves over \(\mathbb Q\) have rank one. Zbl 1315.11045
Bhargava, Manjul; Skinner, Christopher
3
2014
Rational points on elliptic and hyperelliptic curves. Zbl 1373.11045
Bhargava, Manjul
1
2014
On the Davenport-Heilbronn theorems and second order terms. Zbl 1294.11191
Bhargava, Manjul; Shankar, Arul; Tsimerman, Jacob
29
2013
The average size of the 2-Selmer group of Jacobians of hyperelliptic curves having a rational Weierstrass point. Zbl 1303.11072
Bhargava, Manjul; Gross, Benedict H.
14
2013
The density of discriminants of quintic rings and fields. Zbl 1220.11139
Bhargava, Manjul
44
2010
Error estimates for the Davenport-Heilbronn theorems. Zbl 1227.11114
Belabas, Karim; Bhargava, Manjul; Pomerance, Carl
15
2010
On \(P\)-orderings, rings of integer-valued polynomials, and ultrametric analysis. Zbl 1219.11047
Bhargava, Manjul
15
2009
Finite generation properties for various rings of integer-valued polynomials. Zbl 1177.13051
Bhargava, Manjul; Cahen, Paul-Jean; Yeramian, Julie
8
2009
On the average number of octahedral newforms of prime level. Zbl 1206.11049
Bhargava, Manjul; Ghate, Eknath
3
2009
Higher composition laws. IV: The parametrization of quintic rings. Zbl 1173.11058
Bhargava, Manjul
15
2008
The density of discriminants of \(S_3\)-sextic number fields. Zbl 1171.11058
Bhargava, Manjul; Wood, Melanie Matchett
10
2008
Mass formulae for extensions of local fields, and conjectures on the density of number field discriminants. Zbl 1145.11080
Bhargava, Manjul
24
2007
Higher composition laws and applications. Zbl 1129.11049
Bhargava, Manjul
10
2006
The density of discriminants of quartic rings and fields. Zbl 1159.11045
Bhargava, Manjul
66
2005
Higher composition laws. III: The parametrization of quartic rings. Zbl 1169.11045
Bhargava, Manjul
31
2004
Higher composition laws. I: A new view on Gauss composition, and quadratic generalizations. Zbl 1072.11078
Bhargava, Manjul
29
2004
Higher composition laws. II: On cubic analogues of Gauss composition. Zbl 1169.11044
Bhargava, Manjul
22
2004
Gauss composition and generalizations. Zbl 1058.11030
Bhargava, Manjul
2
2002
The factorial function and generalizations. Zbl 0987.05003
Bhargava, Manjul
42
2000
On the Conway-Schneeberger Fifteen Theorem. Zbl 0987.11027
Bhargava, Manjul
40
2000
Factoring Dickson polynomials over finite fields. Zbl 0929.11060
Bhargava, Manjul; Zieve, Michael E.
14
1999
Continuous functions on compact subsets of local fields. Zbl 0979.11054
Bhargava, Manjul; Kedlaya, Kiran S.
9
1999
Generalized factorials and fixed divisors over subsets of a Dedekind domain. Zbl 0931.13004
Bhargava, Manjul
21
1998
\(P\)-orderings and polynomial functions on arbitrary subsets of Dedekind rings. Zbl 0899.13022
Bhargava, Manjul
56
1997
Congruence preservation and polynomial functions from \(\mathbb{Z}_n\) to \(\mathbb{Z}_m\). Zbl 0883.11011
Bhargava, Manjul
3
1997
all top 5

Cited by 416 Authors

20 Bhargava, Manjul
18 Chabert, Jean-Luc
12 Wood, Melanie Matchett
11 Adam, David
9 Cahen, Paul-Jean
9 Oh, Byeong-Kweon
9 Shankar, Arul
9 Thorne, Frank
8 Johnson, Keith Peter
6 Cohen, Henri
6 Fisher, Tom A.
6 Poonen, Bjorn
5 Fares, Youssef
5 Ho, Wei
5 Kala, Vítězslav
5 Kaplan, Nathan
5 Kim, Henry H.
5 Sha, Min
5 Taniguchi, Takashi
4 Cho, Peter Jaehyun
4 Creutz, Brendan
4 Evrard, Sabine
4 Gross, Benedict Hyman
4 Ji, Yun-Seong
4 Ju, Jangwon
4 Lemke Oliver, Robert J.
4 Li, Xiumei
4 Mantilla-Soler, Guillermo
4 Peruginelli, Giulio
4 Thorne, Jack A.
4 Tsimerman, Jacob
4 Wang, Xiaoheng
4 Widmer, Martin
4 Xiao, Stanley Yao
3 Alberts, Brandon
3 Belabas, Karim
3 Boulanger, Jacques
3 Diaz y Diaz, Francisco
3 Earnest, Andrew G.
3 Ellenberg, Jordan S.
3 Kim, Ji Young
3 Klagsbrun, Zev
3 Lagarias, Jeffrey C.
3 Malle, Gunter
3 O’Dorney, Evan M.
3 Olivier, Michel
3 Pierce, Lillian B.
3 Rouse, Jeremy A.
3 Stoll, Michael
3 Thakur, Dinesh S.
3 Varma, Ila
3 Werner, Nicholas J.
3 Williams, Kenneth S.
3 Yeramian, Julie
3 Yucas, Joseph L.
2 Blomer, Valentin
2 Bochnak, Jacek
2 Borsten, Leron
2 Budarina, Natalia Viktorovna
2 Cegielski, Patrick
2 Cremona, John E.
2 Dèbes, Pierre
2 Delaunay, Christophe
2 Duff, Michael J.
2 Evans, Ronald J.
2 Fitzgerald, Robert W.
2 Frisch, Sophie
2 Gao, Xia
2 Greither, Cornelius
2 Grigorieff, Serge
2 Grinberg, Darij
2 Guessarian, Irène
2 Gunawardana, B. L. K.
2 Harron, Piper
2 Harron, Robert
2 Hough, Bob
2 Hough, Robert D.
2 Ishitsuka, Yasuhiro
2 Ito, Tetsushi
2 Jacobson, Michael John jun.
2 Jones, John William
2 Kane, Ben
2 Kane, Daniel M.
2 Kedlaya, Kiran Sridhara
2 Kim, Byeong Moon
2 Kim, Myeong Jae
2 Kim, Myung-Hwan
2 Köklüce, Bülent
2 König, Joachim
2 Le Boudec, Pierre
2 Lemmermeyer, Franz Josef
2 Lipnowski, Michael
2 Mazur, Barry
2 Miller, Stephen D.
2 Miller, Steven J.
2 Park, Jennifer
2 Petrov, Fedor Vladimirovich
2 Pollack, Aaron
2 Rains, Eric M.
2 Roberts, David Peter
...and 316 more Authors
all top 5

Cited in 100 Serials

48 Journal of Number Theory
23 International Journal of Number Theory
18 Journal of Algebra
14 Finite Fields and their Applications
13 Proceedings of the American Mathematical Society
13 The Ramanujan Journal
12 Compositio Mathematica
9 Journal de Théorie des Nombres de Bordeaux
8 Duke Mathematical Journal
8 Transactions of the American Mathematical Society
8 Research in the Mathematical Sciences
8 Research in Number Theory
7 Journal of Pure and Applied Algebra
6 Mathematics of Computation
6 Advances in Mathematics
6 Journal of the European Mathematical Society (JEMS)
5 Communications in Algebra
5 Journal of the American Mathematical Society
5 Annals of Mathematics. Second Series
4 American Mathematical Monthly
4 Inventiones Mathematicae
4 Mathematische Annalen
4 Mathematische Zeitschrift
4 Algebra & Number Theory
4 Forum of Mathematics, Sigma
3 Mathematical Proceedings of the Cambridge Philosophical Society
3 Acta Arithmetica
3 Bulletin of the London Mathematical Society
3 Monatshefte für Mathematik
3 Bulletin of the American Mathematical Society. New Series
3 Experimental Mathematics
3 Journal of Algebraic Combinatorics
3 LMS Journal of Computation and Mathematics
3 Actes des Rencontres du C.I.R.M.
2 Bulletin of the Australian Mathematical Society
2 Communications in Mathematical Physics
2 Israel Journal of Mathematics
2 Annales de l’Institut Fourier
2 Journal of Approximation Theory
2 Journal of Combinatorial Theory. Series A
2 Journal of the Korean Mathematical Society
2 Journal für die Reine und Angewandte Mathematik
2 Manuscripta Mathematica
2 Mathematika
2 Documenta Mathematica
2 Transformation Groups
2 Integers
2 Journal of the Australian Mathematical Society
2 Journal of the Institute of Mathematics of Jussieu
1 Communications on Pure and Applied Mathematics
1 Discrete Mathematics
1 Journal d’Analyse Mathématique
1 Journal of Mathematical Physics
1 Letters in Mathematical Physics
1 Lithuanian Mathematical Journal
1 Linear and Multilinear Algebra
1 Mathematics Magazine
1 Algebra Universalis
1 Applied Mathematics and Computation
1 Archiv der Mathematik
1 Bulletin de la Société Mathématique de France
1 Canadian Journal of Mathematics
1 Commentarii Mathematici Helvetici
1 Glasgow Mathematical Journal
1 Illinois Journal of Mathematics
1 Journal of the London Mathematical Society. Second Series
1 Michigan Mathematical Journal
1 Pacific Journal of Mathematics
1 Proceedings of the London Mathematical Society. Third Series
1 European Journal of Combinatorics
1 Geometric and Functional Analysis. GAFA
1 L’Enseignement Mathématique. 2e Série
1 Journal de Mathématiques Pures et Appliquées. Neuvième Série
1 Linear Algebra and its Applications
1 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics
1 Journal of Mathematical Sciences (New York)
1 St. Petersburg Mathematical Journal
1 The Electronic Journal of Combinatorics
1 The New York Journal of Mathematics
1 Séminaire Lotharingien de Combinatoire
1 Taiwanese Journal of Mathematics
1 Journal of Group Theory
1 Annals of Combinatorics
1 Physical Review Letters
1 Portugaliae Mathematica. Nova Série
1 Journal of Algebra and its Applications
1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
1 Proceedings of the Steklov Institute of Mathematics
1 The College Mathematics Journal
1 European Journal of Pure and Applied Mathematics
1 Involve
1 Journal of \(K\)-Theory
1 Journal of Commutative Algebra
1 The Review of Symbolic Logic
1 Science China. Mathematics
1 Forum of Mathematics, Pi
1 Annales Mathématiques du Québec
1 Arnold Mathematical Journal
1 Proceedings of the American Mathematical Society. Series B
1 Tunisian Journal of Mathematics
all top 5

Cited in 38 Fields

299 Number theory (11-XX)
72 Commutative algebra (13-XX)
63 Algebraic geometry (14-XX)
21 Group theory and generalizations (20-XX)
20 Field theory and polynomials (12-XX)
14 Combinatorics (05-XX)
14 Linear and multilinear algebra; matrix theory (15-XX)
10 Nonassociative rings and algebras (17-XX)
6 Topological groups, Lie groups (22-XX)
5 Associative rings and algebras (16-XX)
5 Quantum theory (81-XX)
4 History and biography (01-XX)
4 \(K\)-theory (19-XX)
4 Algebraic topology (55-XX)
4 Probability theory and stochastic processes (60-XX)
3 Functional analysis (46-XX)
3 Convex and discrete geometry (52-XX)
3 Relativity and gravitational theory (83-XX)
2 General and overarching topics; collections (00-XX)
2 Functions of a complex variable (30-XX)
2 Manifolds and cell complexes (57-XX)
1 Mathematical logic and foundations (03-XX)
1 General algebraic systems (08-XX)
1 Category theory; homological algebra (18-XX)
1 Measure and integration (28-XX)
1 Potential theory (31-XX)
1 Several complex variables and analytic spaces (32-XX)
1 Special functions (33-XX)
1 Partial differential equations (35-XX)
1 Dynamical systems and ergodic theory (37-XX)
1 Approximations and expansions (41-XX)
1 Differential geometry (53-XX)
1 General topology (54-XX)
1 Numerical analysis (65-XX)
1 Statistical mechanics, structure of matter (82-XX)
1 Operations research, mathematical programming (90-XX)
1 Biology and other natural sciences (92-XX)
1 Information and communication theory, circuits (94-XX)

Citations by Year

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