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 2019Show all

2 papers · 1 filter

math.NT2019★ 13 cited

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

Ananth N. Shankar, Arul Shankar, Yunqing Tang +1

Given a K3 surface $X$ over a number field $K$ with potentially good reduction everywhere, we prove that the set of primes of $K$ where the geometric Picard rank jumps is infinite.…

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…