Goldfeld conjecture for non-hyperelliptic direction
Number Theory
2026-02-26 v1
Abstract
Since the curve has a large automorphism group, there exist twist families arising from non-hyperelliptic directions. In this paper, we give an explicit upper bound on the average analytic rank of such a family, assuming the generalized Riemann hypothesis for the -functions. Also, we propose an analogue of the Goldfeld conjecture for the family following Katz--Sarnak philosophy.
Cite
@article{arxiv.2602.21985,
title = {Goldfeld conjecture for non-hyperelliptic direction},
author = {Keunyoung Jeong and Junyeong Park},
journal= {arXiv preprint arXiv:2602.21985},
year = {2026}
}