A. Shankar

发表

Exceptional jumps of Picard ranks of reductions of K3 surfaces over number fields

Yunqing Tang, A. Shankar, A. Shankar, 2019, Forum of Mathematics, Pi.

Odd degree number fields with odd class number

A. Shankar, Ila Varma, Wei Ho, 2016, 1603.06269.

The average elliptic curve has few integral

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

Central values of zeta functions of non-Galois cubic fields

Nicolas Templier, Anders Sodergren, A. Shankar, 2021, 2107.10900.

Geometry-of-numbers methods in the cusp

A. Swaminathan, A. Shankar, Ila Varma, 2021, 2110.09466.

On the Davenport–Heilbronn theorems and second order terms

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

Low-lying zeros of certain families of Artin L-functions

Nicolas Templier, A. Södergren, A. Shankar, 2015 .

Average size of the 2-Selmer group of Jacobians of monic even hyperelliptic curves

Xiaoheng Wang, A. Shankar, 2013, 1307.3531.

On two theta function identities of Ramanujan

K. R. Vasuki, A. Shankar, 2022, Indian Journal of Pure and Applied Mathematics.

SATO–TATE EQUIDISTRIBUTION OF CERTAIN FAMILIES OF ARTIN $L$ -FUNCTIONS

Nicolas Templier, A. Södergren, A. Shankar, 2015, Forum of Mathematics, Sigma.

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 Manjul Bhargava and Arul Shankar]

B. Poonen, A. Shankar, 2012 .

AVERAGE RANK OF ELLIPTIC CURVES [ after

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

Counting integral points on symmetric varieties with applications to arithmetic statistics

A. Swaminathan, A. Shankar, Artane Siad, 2023, 2304.01050.

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.

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.

COUNTING $S_5$ -FIELDS WITH A POWER SAVING ERROR TERM

Jacob Tsimerman, Arul Shankar, Jacob Tsimerman, 2013, Forum of Mathematics, Sigma.

On the Davenport–Heilbronn theorems and second order terms

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

Rational points on hyperelliptic curves having a marked non-Weierstrass point

Xiaoheng Wang, A. Shankar, 2017, Compositio Mathematica.

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.

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.

The number of $D_4$-fields ordered by conductor

Kevin H. Wilson, Arul Shankar, S. Ali Altug, 2021 .

The number of quartic $D_4$-fields ordered by conductor

Kevin H. Wilson, A. Shankar, Ila Varma, 2017, 1704.01729.

Non-trivial bounds on 2, 3, 4, and 5-torsion in class groups of number fields, conditional on standard $L$-function conjectures

Jacob Tsimerman, A. Shankar, 2021, 2112.12949.

Central values of zeta functions of non-Galois cubic fields

Nicolas Templier, Anders Sodergren, A. Shankar, 2021, 2107.10900.

Abelian surfaces over finite fields with prescribed groups

C. David, Ethan Smith, D. Garton, 2013, 1307.0863.

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

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

On the asymptotics of cubic fields ordered by general invariants

F. Thorne, A. Shankar, 2022, 2207.06514.

Heuristics for the asymptotics of the number of Sn$S_n$ ‐number fields

Jacob Tsimerman, A. Shankar, 2020, Journal of the London Mathematical Society.