On the non-vanishing of modular $L$-values and fourier coefficients of cusp forms

Jun Hwi Min

Type: Preprint

Publication Date: 2022-02-07

Citations: 0

Abstract

We prove a non-vanishing result of modular L-values with quadratic twists, where the quadratic discriminants are in a short interval. Using this fact and Waldspurger's theorem, we improve the results of Balog-Ono[The chebotarev density theorem in short intervals and some questions of Serre, Journal of number theory. 91(2):356-371(2001)] on the non-vanishing of Fourier coefficients of half-integral weight eigenform.

Locations

arXiv (Cornell University) - View - PDF

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