M. Bhargava

发表

A positive proportion of locally soluble Thue equations are globally insoluble

S. Akhtari, M. Bhargava, 2016 .

On the Davenport–Heilbronn theorems and second order terms

Jacob Tsimerman, M. Bhargava, Arul Shankar, 2010, 1005.0672.

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

B. Gross, M. Bhargava, Xiaoheng Wang, 2017 .

A positive proportion of locally soluble hyperelliptic curves over ℚ have no point over any odd degree extension

B. Gross, M. Bhargava, Xiaoheng Wang, 2013, 1310.7692.

A positive proportion of locally soluble hyperelliptic curves over ℚ have no point over any odd degree extension

B. Gross, M. Bhargava, Xiaoheng Wang, 2013, 1310.7692.

HEURISTICS FOR THE ARITHMETIC OF ELLIPTIC CURVES

H. Lenstra, J. Voight, M. Bhargava, 2017 .

The proportion of genus one curves over $\mathbb{Q}$ defined by a binary quartic that everywhere locally have a point

J. Cremona, T. Fisher, M. Bhargava, 2020, 2004.12085.

The proportion of genus one curves over ℚ defined by a binary quartic that everywhere locally have a point

J. Cremona, T. Fisher, M. Bhargava, 2020, International Journal of Number Theory.

A positive proportion of Thue equations fail the integral Hasse principle

S. Akhtari, M. Bhargava, 2016, American Journal of Mathematics.

Most hyperelliptic curves over Q have no rational points

M. Bhargava, 2013, 1308.0395.

A positive proportion of locally soluble hyperelliptic curves over $\mathbb Q$ have no point over any odd degree extension

B. Gross, T. Dokchitser, M. Bhargava, 2013 .

Universal quadratic forms and the 290-Theorem

M. Bhargava, J. Hanke, Jonathan Hanke, 2011 .

The average elliptic curve has few integral

Katherine E. Stange, Henry Cohn, J. Silverman, 2014 .

On the mean number of $2$-torsion elements in the class groups, narrow class groups, and ideal groups of cubic orders and fields

M. Bhargava, Ila Varma, 2014, 1402.5738.

The geometric sieve and the density of squarefree values of invariant polynomials

M. Bhargava, 2014, 1402.0031.

Mass Formulae for Extensions of Local Fields, and Conjectures on the Density of Number Field Discriminants

M. Bhargava, 2007 .

Hermite equivalence of polynomials

J. Evertse, M. Bhargava, K. GyHory, 2021, 2109.02932.

What is the probability that a random integral quadratic form in nvariables has an integral zero? International

J. Keating, J. Cremona, T. Fisher, 2015 .

On the number of monogenizations of a quartic order (with an appendix by Shabnam Akhtari)

M. Bhargava, 2021, Publicationes Mathematicae Debrecen.

3-Isogeny Selmer groups and ranks of Abelian varieties in quadratic twist families over a number field

M. Bhargava, A. Shnidman, Z. Klagsbrun, 2017, Duke Mathematical Journal.

A positive proportion of plane cubics fail the Hasse principle

M. Bhargava, 2014, 1402.1131.

On the Davenport–Heilbronn theorems and second order terms

Jacob Tsimerman, M. Bhargava, A. Shankar, 2012, Inventiones mathematicae.

Galois groups of random integer polynomials and van der Waerden's Conjecture

M. Bhargava, 2021, 2111.06507.

Integers expressible as the sum of two rational cubes

M. Bhargava, A. Shnidman, Levent Alpoge, 2022, 2210.10730.

Error estimates for the Davenport-Heilbronn theorems

C. Pomerance, K. Belabas, M. Bhargava, 2010 .

A positive proportion of cubic fields are not monogenic yet have no local obstruction to being so

M. Bhargava, A. Shnidman, Levent Alpoge, 2020, 2011.01186.

The equidistribution of lattice shapes of rings of integers in cubic, quartic, and quintic number fields

M. Bhargava, Piper Harron, 2013, Compositio Mathematica.

On the classification of rings of “ small ” rank

M. Bhargava, 2009 .

The density of discriminants of quartic rings and fields

Manjul Bhargava, M. Bhargava, 2005, 1005.5578.

Finite generation properties for various rings of integer-valued polynomials

M. Bhargava, Paul Jean Cahen, Julie Yeramian, 2009 .

The local-global principle for integral points on stacky curves

B. Poonen, M. Bhargava, 2020, Journal of Algebraic Geometry.

Arithmetic invariant theory II: Pure inner forms and obstructions to the existence of orbits

B. Gross, M. Bhargava, Xiaoheng Wang, 2015 .

A positive proportion of elliptic curves over Q have rank one

M. Bhargava, C. Skinner, 2014, 1401.0233.

Arithmetic invariant theory II

B. Gross, M. Bhargava, Xiaoheng Wang, 2013, 1310.7689.

ORBIT PARAMETRIZATIONS FOR K3 SURFACES

Abhinav Kumar, M. Bhargava, Wei Ho, 2013, Forum of Mathematics, Sigma.

The Factorial Function and Generalizations

Manjul Bhargava, M. Bhargava, 2000, Am. Math. Mon..

P-orderings and polynomial functions on arbitrary subsets of Dedekind rings.

Manjul Bhargava, M. Bhargava, 1997 .

On P-orderings, rings of integer-valued polynomials, and ultrametric analysis

M. Bhargava, 2009 .

Continuous functions on compact subsets of local fields

Kiran S. Kedlaya, Manjul Bhargava, K. Kedlaya, 1999 .

(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.

B. Gross, M. Bhargava, Xiaoheng Wang, 2017 .

Pencils of quadrics and the arithmetic of hyperelliptic curves

B. Gross, M. Bhargava, Xiaoheng Wang, 2013 .

Higher composition laws I: A new view on Gauss composition, and quadratic generalizations

Manjul Bhargava, M. Bhargava, 2004 .

Varieties over finite and local fields 11 S 15 Ramification and extension theory 11 S 80 Other

M. Bhargava, 2022 .

The average size of the 3‐isogeny Selmer groups of elliptic curves y2=x3+k

N. Elkies, M. Bhargava, A. Shnidman, 2016, Journal of the London Mathematical Society.

Binary quartic forms having bounded invariants, and the boundedness of the average rank of elliptic curves

M. Bhargava, A. Shankar, 2010, 1006.1002.

The average elliptic curve has few integral points

Katherine E. Stange, Henry Cohn, J. Silverman, 2014 .

AVERAGE RANK OF ELLIPTIC CURVES [ after

B. Poonen, M. Bhargava, A. Shankar, 2012 .

On average sizes of Selmer groups and ranks in families of elliptic curves having marked points

M. Bhargava, Wei Ho, 2022, 2207.03309.

Elements of given order in Tate–Shafarevich groups of abelian varieties in quadratic twist families

M. Bhargava, A. Shnidman, Z. Klagsbrun, 2019, 1904.00116.

Squarefree values of polynomial discriminants II

M. Bhargava, Xiaoheng Wang, A. Shankar, 2022, 2207.05592.

Squarefree values of polynomial discriminants I

M. Bhargava, Xiaoheng Wang, A. Shankar, 2016, Inventiones mathematicae.

Coregular spaces and genus one curves

M. Bhargava, Wei Ho, 2013, 1306.4424.

Ternary cubic forms having bounded invariants, and the existence of a positive proportion of elliptic curves having rank 0

Manjul Bhargava, Arul Shankar, M. Bhargava, 2010, 1007.0052.

Higher composition laws III: The parametrization of quartic rings

Manjul Bhargava, M. Bhargava, 2004 .

Modeling the distribution of ranks, Selmer groups, and Shafarevich-Tate groups of elliptic curves

D. Kane, H. Lenstra, E. Rains, 2013, 1304.3971.

What is the probability that a random integral quadratic form in n variables has an integral zero

J. Keating, J. Cremona, T. Fisher, 2015, 1502.05992.

The proportion of plane cubic curves over ${\mathbb Q}$ that everywhere locally have a point

J. Cremona, T. Fisher, M. Bhargava, 2013, 1311.5578.

Bounds on 2-torsion in class groups of number fields and integral points on elliptic curves

Jacob Tsimerman, M. Bhargava, Takashi Taniguchi, 2017, Journal of the American Mathematical Society.

What is the probability that a random integral quadratic form in $n$ variables is isotropic?

J. Cremona, T. Fisher, M. Bhargava, 2013, 1311.5543.

The average size of the 5-Selmer group of elliptic curves is 6, and the average rank is less than 1

M. Bhargava, A. Shankar, 2013, 1312.7859.

Arithmetic invariant theory

B. Gross, M. Bhargava, 2012, 1206.4774.

Improved error estimates for the Davenport–Heilbronn theorems

M. Bhargava, Takashi Taniguchi, F. Thorne, 2021, Mathematische Annalen.

Higher composition laws and applications

M. Bhargava, 2006 .

Geometry-of-numbers methods over global fields I: Prehomogeneous vector spaces

Manjul Bhargava, Xiaoheng Wang, Arul Shankar, 2015, 1512.03035.

THE DENSITY OF DISCRIMINANTS OF S3-SEXTIC NUMBER FIELDS

M. Bhargava, M. Wood, 2007 .

Higher composition laws

Manjul Bhargava, M. Bhargava, 2001 .

Hermite equivalence of polynomials

J. Evertse, M. Bhargava, A. Swaminathan, 2021, Acta Arithmetica.

Gauss Composition and Generalizations

Manjul Bhargava, M. Bhargava, 2002, ANTS.