English

The average analytic rank of elliptic curves with prescribed level structure

Number Theory 2025-09-22 v3

Abstract

Assuming the Hasse--Weil conjecture and the generalized Riemann hypothesis for the LL-functions of the elliptic curve, we give an upper bound of the average analytic rank of elliptic curves over the number field with a level structure such that the corresponding compactified moduli stack is representable by the projective line.

Keywords

Cite

@article{arxiv.2312.05817,
  title  = {The average analytic rank of elliptic curves with prescribed level structure},
  author = {Peter J. Cho and Keunyoung Jeong and Junyeong Park},
  journal= {arXiv preprint arXiv:2312.05817},
  year   = {2025}
}