Goldfeld conjecture for non-hyperelliptic direction

Fuente: arXiv
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Hauptverfasser: Jeong, Keunyoung, Park, Junyeong
Format: Preprint
Veröffentlicht: 2026
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author Jeong, Keunyoung
Park, Junyeong
author_facet Jeong, Keunyoung
Park, Junyeong
contents Since the curve $y^2 = x^6+1$ 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 $L$-functions. Also, we propose an analogue of the Goldfeld conjecture for the family following Katz--Sarnak philosophy.
format Preprint
id arxiv_https___arxiv_org_abs_2602_21985
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Goldfeld conjecture for non-hyperelliptic direction
Jeong, Keunyoung
Park, Junyeong
Number Theory
Since the curve $y^2 = x^6+1$ 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 $L$-functions. Also, we propose an analogue of the Goldfeld conjecture for the family following Katz--Sarnak philosophy.
title Goldfeld conjecture for non-hyperelliptic direction
topic Number Theory
url https://arxiv.org/abs/2602.21985