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 -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}
}