2022/11/01 by Keunyoung Jeong, Jeong, Keunyoung, Yeong-Wook Kwon +3
Mathematics · #11F27 #11G10 #11G40 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2211.00305
openalex publication_date 2022/11/01 · openalex created_date 2022/11/07 · openalex updated_date 2026/07/28
In this paper, we show the nonvanishing of some Hecke characters on cyclotomic fields. The main ingredient of this paper is a computation of eigenfunctions and the action of Weil representation at some primes including the primes above 2. As an application, we show that for each isogeny factor of the Jacobian of the p-th Fermat curve where 2 is a quadratic residue modulo p, there are infinitely many twists whose analytic rank is zero. Also, for a certain hyperelliptic curve over the 11-th cyclotomic field whose Jacobian has complex multiplication, there are infinitely many twists whose analytic rank is zero.