A. Shankar

activity

20102026

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

45 citations · 246 across the 34 of their papers we have counts for

collaborators

Showing 2021Show all

4 papers · 1 filter

math.NT2021

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

Arul Shankar, Jacob Tsimerman

We prove new conditional bounds on the the $m$ -torsion of class groups of number fields of any fixed degree, for $m = 2$ , $3$ , $4$ , and $5$ . Our methods first recast the problem in t…

math.NT2021★ 1 cited

The second moment of the size of the $2$ -Selmer group of elliptic curves

Manjul Bhargava, Arul Shankar, Ashvin Swaminathan

In this paper, we prove that when elliptic curves over $Q$ are ordered by height, the second moment of the size of the $2$ -Selmer group is at most $15$ . This confirms a co…

math.NT2021

Geometry-of-numbers methods in the cusp

Arul Shankar, Artane Siad, Ashvin Swaminathan +1

In this article, we develop new methods for counting integral orbits having bounded invariants that lie inside the cusps of fundamental domains for coregular representations. We il…

math.NT2021

Central values of zeta functions of non-Galois cubic fields

Arul Shankar, Anders Södergren, Nicolas Templier

The Dedekind zeta functions of infinitely many non-Galois cubic fields have negative central values.

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

The second moment of the size of the 2-Selmer group of elliptic curves

Geometry-of-numbers methods in the cusp

Central values of zeta functions of non-Galois cubic fields

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

The second moment of the size of the $2$ -Selmer group of elliptic curves