A. Shankar

activity

20192021

most citedThe mean number of 2-torsion elements in the class groups of

n

-monogenized cubic fields

4 citations · 6 across the 4 of their papers we have counts for

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4 papers · 1 filter

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.NT2020★ 4 cited

The mean number of 2-torsion elements in the class groups of $n$ -monogenized cubic fields

Manjul Bhargava, Jonathan Hanke, Arul Shankar

We prove that, on average, the monogenicity or $n$ -monogenicity of a cubic field has an altering effect on the behavior of the 2-torsion in its class group.

math.NT2020

Heuristics for the asymptotics of the number of $S_{n}$ -number fields

Arul Shankar, Jacob Tsimerman

We give a heuristic argument supporting conjectures of Bhargava on the asymptotics of the number of $S_{n}$ -number fields having bounded discriminant. We then make our arguments rigo…

math.NT2019★ 1 cited

Families of elliptic curves ordered by conductor

Ananth N. Shankar, Arul Shankar, Xiaoheng Wang

In this article, we study the family of elliptic curves $E / Q$ , having good reduction at $2$ and $3$ , and whose $j$ -invariants are small. Within this set of elliptic curves…

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

The mean number of 2-torsion elements in the class groups of n-monogenized cubic fields

Heuristics for the asymptotics of the number of Sn​-number fields

Families of elliptic curves ordered by conductor

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

The mean number of 2-torsion elements in the class groups of $n$ -monogenized cubic fields

Heuristics for the asymptotics of the number of $S_{n}$ -number fields