Secondary terms in the first moment of $|{\rm Sel}_2(E)|$

Arul Shankar; Takashi Taniguchi

Secondary terms in the first moment of $|{\rm Sel}_2(E)|$

Number Theory 2024-12-03 v1

Authors: Arul Shankar , Takashi Taniguchi

Abstract

We prove the existence of secondary terms of order $X^{3/4}$ , with power saving error terms, in the counting functions of $|{\rm Sel}_2(E)|$ , the 2-Selmer group of E, for elliptic curves E having height bounded by X. This is the first improvement on the error term of $o(X^{5/6})$ , proved by Bhargava--Shankar, where the primary term of order $X^{5/6}$ for this counting function was obtained.

Keywords

2-Selmer group elliptic curves first moment secondary terms height counting functions error terms

Cite

@article{arxiv.2412.00995,
  title  = {Secondary terms in the first moment of $|{\rm Sel}_2(E)|$},
  author = {Arul Shankar and Takashi Taniguchi},
  journal= {arXiv preprint arXiv:2412.00995},
  year   = {2024}
}

Related papers

View all related →