# Manjul Bhargava

#2,301

Most Influential Person Now

Indo-Canadian mathematician

## Manjul Bhargava's AcademicInfluence.com Rankings

Manjul Bhargavamathematics Degrees

Mathematics

#153

World Rank

#366

Historical Rank

Number Theory

#14

World Rank

#29

Historical Rank

Geometry

#23

World Rank

#49

Historical Rank

Measure Theory

#3386

World Rank

#3998

Historical Rank

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Mathematics

## Manjul Bhargava's Degrees

- PhD Mathematics Princeton University

## Why Is Manjul Bhargava Influential?

(Suggest an Edit or Addition)According to Wikipedia, Manjul Bhargava is a Canadian-American mathematician. He is the Brandon Fradd, Class of 1983, Professor of Mathematics at Princeton University, the Stieltjes Professor of Number Theory at Leiden University, and also holds Adjunct Professorships at the Tata Institute of Fundamental Research, the Indian Institute of Technology Bombay, and the University of Hyderabad. He is known primarily for his contributions to number theory.

## Manjul Bhargava's Published Works

### Published Works

- The density of discriminants of quartic rings and fields (2005) (259)
- Binary quartic forms having bounded invariants, and the boundedness of the average rank of elliptic curves (2010) (192)
- Higher composition laws I: A new view on Gauss composition, and quadratic generalizations (2004) (159)
- Higher composition laws III: The parametrization of quartic rings (2004) (149)
- Ternary cubic forms having bounded invariants, and the existence of a positive proportion of elliptic curves having rank 0 (2010) (131)
- On the Davenport–Heilbronn theorems and second order terms (2010) (126)
- Higher composition laws II: On cubic analogues of Gauss composition (2004) (114)
- P-orderings and polynomial functions on arbitrary subsets of Dedekind rings. (1997) (110)
- Mass Formulae for Extensions of Local Fields, and Conjectures on the Density of Number Field Discriminants (2007) (94)
- The average size of the 2-Selmer group of Jacobians of hyperelliptic curves having a rational Weierstrass point (2012) (91)
- Higher composition laws IV: The parametrization of quintic rings (2008) (84)
- Higher composition laws (2001) (82)
- Universal quadratic forms and the 290-Theorem (2011) (73)
- Modeling the distribution of ranks, Selmer groups, and Shafarevich-Tate groups of elliptic curves (2013) (71)
- The average size of the 5-Selmer group of elliptic curves is 6, and the average rank is less than 1 (2013) (65)
- The geometric sieve and the density of squarefree values of invariant polynomials (2014) (63)
- Bounds on 2-torsion in class groups of number fields and integral points on elliptic curves (2017) (54)
- The Factorial Function and Generalizations (2000) (52)
- Coregular spaces and genus one curves (2013) (48)
- Geometry-of-numbers methods over global fields I: Prehomogeneous vector spaces (2015) (47)
- Arithmetic invariant theory (2012) (46)
- Most hyperelliptic curves over Q have no rational points (2013) (45)
- Squarefree values of polynomial discriminants I (2016) (41)
- Generalized Factorials and Fixed Divisors over Subsets of a Dedekind Domain (1998) (38)
- Error estimates for the Davenport-Heilbronn theorems (2010) (37)
- The average number of elements in the 4-Selmer groups of elliptic curves is 7 (2013) (37)
- A majority of elliptic curves over $\mathbb Q$ satisfy the Birch and Swinnerton-Dyer conjecture (2014) (36)
- THE DENSITY OF DISCRIMINANTS OF S3-SEXTIC NUMBER FIELDS (2007) (35)
- On the mean number of $2$-torsion elements in the class groups, narrow class groups, and ideal groups of cubic orders and fields (2014) (34)
- A positive proportion of plane cubics fail the Hasse principle (2014) (34)
- The equidistribution of lattice shapes of rings of integers in cubic, quartic, and quintic number fields (2013) (33)
- A positive proportion of locally soluble hyperelliptic curves over ℚ have no point over any odd degree extension (2013) (33)
- Factoring Dickson Polynomials over Finite Fields (1999) (33)
- The mean number of 3‐torsion elements in the class groups and ideal groups of quadratic orders (2014) (30)
- On the number of cubic orders of bounded discriminant having automorphism group $C_3$, and related problems (2012) (27)
- Higher composition laws and applications (2006) (23)
- On P-orderings, rings of integer-valued polynomials, and ultrametric analysis (2009) (23)
- What is the probability that a random integral quadratic form in n variables has an integral zero (2015) (23)
- Pencils of quadrics and the arithmetic of hyperelliptic curves (2013) (22)
- A positive proportion of elliptic curves over Q have rank one (2014) (21)
- On a notion of "Galois closure" for extensions of rings (2010) (18)
- Continuous functions on compact subsets of local fields (1999) (17)
- Gauss Composition and Generalizations (2002) (17)
- The average size of the 3‐isogeny Selmer groups of elliptic curves y2=x3+k (2016) (16)
- Congruence preservation and polynomial functions from Zn to Zm (1997) (15)
- 3-Isogeny Selmer groups and ranks of Abelian varieties in quadratic twist families over a number field (2017) (14)
- The proportion of plane cubic curves over ${\mathbb Q}$ that everywhere locally have a point (2013) (13)
- On the average number of octahedral newforms of prime level (2009) (13)
- On average sizes of Selmer groups and ranks in families of elliptic curves having marked points (2022) (12)
- Galois groups of random integer polynomials and van der Waerden's Conjecture (2021) (12)
- Arithmetic invariant theory II: Pure inner forms and obstructions to the existence of orbits (2015) (11)
- The mean number of 2-torsion elements in the class groups of $n$-monogenized cubic fields (2020) (11)
- ORBIT PARAMETRIZATIONS FOR K3 SURFACES (2013) (10)
- HEURISTICS FOR THE ARITHMETIC OF ELLIPTIC CURVES (2017) (10)
- Finite generation properties for various rings of integer-valued polynomials (2009) (10)
- Improved error estimates for the Davenport-Heilbronn theorems (2021) (9)
- A positive proportion of quartic fields are not monogenic yet have no local obstruction to being so (2020) (8)
- A positive proportion of Thue equations fail the integral Hasse principle (2016) (8)
- The local-global principle for integral points on stacky curves (2020) (7)
- Elements of given order in Tate–Shafarevich groups of abelian varieties in quadratic twist families (2019) (6)
- The proportion of genus one curves over ℚ defined by a binary quartic that everywhere locally have a point (2020) (6)
- A positive proportion of elliptic curves over $\mathbb{Q}$ have rank one (2014) (5)
- Integers expressible as the sum of two rational cubes (2022) (5)
- On the number of monogenizations of a quartic order (with an appendix by Shabnam Akhtari) (2021) (4)
- An improvement on Schmidt’s bound on the number of number fields of bounded discriminant and small degree (2022) (3)
- A positive proportion of locally soluble hyperelliptic curves over $\mathbb Q$ have no point over any odd degree extension (2013) (2)
- On the Davenport–Heilbronn theorems and second order terms (2012) (2)
- The second moment of the size of the $2$-Selmer group of elliptic curves (2021) (2)
- Finite Simple Groups: Thirty Years of the Atlas and Beyond (2017) (2)
- On the number of integral binary n$n$ ‐ic forms having bounded Julia invariant (2013) (2)
- The proportion of genus one curves over $\mathbb{Q}$ defined by a binary quartic that everywhere locally have a point (2020) (2)
- Arithmetic invariant theory II (2013) (2)
- Squarefree values of polynomial discriminants II (2022) (2)
- The density of polynomials of degree n$n$ over Zp${\mathbb {Z}}_p$ having exactly r$r$ roots in Qp${\mathbb {Q}}_p$ (2022) (1)
- A positive proportion of locally soluble Thue equations are globally insoluble (2016) (1)
- On the classification of rings of “ small ” rank (2009) (1)
- Rational points on elliptic and hyperelliptic curves (2014) (1)
- What is the probability that a random integral quadratic form in $n$ variables is isotropic? (2013) (1)
- Analysis, Spectra, and Number Theory: A Conference in Honor of Peter Sarnak’s 60th Birthday December 15-19, 2014 (2015) (0)
- Solutions to the 64th William Lowell Putnam Mathematical Competition Saturday, December 6, 2003 (2003) (0)
- Solutions to the 76 th William Lowell Putnam Mathematical Competition Saturday , December 5 , 2015 (2016) (0)
- A POSITIVE PROPORTION OF LOCALLY SOLUBLE HYPERELLIPTIC CURVES OVER Q HAVE NO POINT OVER ANY ODD DEGREE EXTENSION MANJUL BHARGAVA, BENEDICT H. GROSS, AND XIAOHENG WANG, WITH AN APPENDIX BY TIM DOKCHITSER AND VLADIMIR DOKCHITSER (2017) (0)
- The Work of Manjul Bhargava (2014) (0)
- CUBIC RINGS AND FORMS (2010) (0)
- Foreword (2019) (0)
- Foreword (2019) (0)
- The average elliptic curve has few integral (2014) (0)
- Factoring Dickson Polynomials over Nite Elds (1997) (0)
- The density of polynomials of degree 𝒏 over ℤ 𝒑 having exactly 𝒓 roots in ℚ 𝒑 (2022) (0)
- What is the probability that a random integral quadratic form in nvariables has an integral zero? International (2015) (0)
- Solutions to the 82nd William Lowell Putnam Mathematical Competition Saturday, December 4, 2021 (2021) (0)
- Hermite equivalence of polynomials (2021) (0)
- The density of polynomials of degree $n$ over $\mathbb{Z}_p$ having exactly $r$ roots in $\mathbb{Q}_p$ (2021) (0)
- John Horton Conway (1937–2020) (2020) (0)
- Mass Formulas for Z p and F p Algebras (2012) (0)
- Solutions to the 62 nd William Lowell Putnam Mathematical Competition Saturday , December 1 , 2001 (2013) (0)
- AVERAGE RANK OF ELLIPTIC CURVES [ after (2012) (0)
- October 2014 Cover English (2014) (0)
- A proof of van der Waerden’s Conjecture on random Galois groups of polynomials (2023) (0)
- (2017). A positive proportion of locally soluble hyperelliptic curves over Q have no point over any odd degree extension. Journal of the American Mathematical Society, 30(2), 451-493. (2017) (0)
- Solutions to the 57 th William Lowell Putnam Mathematical Competition Saturday , December 7 , 1996 (2013) (0)
- PARAMETRIZATION OF RINGS OF SMALL RANK : COURSE DESCRIPTION (2008) (0)
- Solutions to the 66 th William Lowell Putnam Mathematical Competition Saturday , December 3 , 2005 (2005) (0)
- Clay Research Conference (2007) (0)
- Solutions to the 68 th William Lowell Putnam Mathematical Competition Saturday , December 1 , 2007 (2007) (0)
- John Horton Conway (1937–2020) (2020) (0)
- Solutions to the 60th William Lowell Putnam Mathematical Competition Saturday, December 4, 1999 (2015) (0)
- The average elliptic curve has few integral points (2014) (0)
- Solutions to the 81 st William Lowell Putnam Mathematical Competition Saturday (2018) (0)
- Varieties over finite and local fields 11 S 15 Ramification and extension theory 11 S 80 Other (2022) (0)
- INTRODUCTION: PRE-HOMOGENEOUS SPACES (2011) (0)

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## What Schools Are Affiliated With Manjul Bhargava?

Manjul Bhargava is affiliated with the following schools: