Zeros of the Derivatives of $L$-functions Attached to Cusp Forms

Volume 64 / 2016

Yoshikatsu Yashiro Bulletin Polish Acad. Sci. Math. 64 (2016), 147-164 MSC: Primary 11M26; Secondary 11N75. DOI: 10.4064/ba8068-10-2016 Published online: 27 October 2016

Abstract

Let $f$ be a holomorphic cusp form of weight $k$ with respect to $\mathrm {SL}_2(\mathbb {Z})$ which is a normalized Hecke eigenform, and $L_f(s)$ the $L$-function attached to $f$. We shall give a relation between the number of zeros of $L_f(s)$ and of the derivatives of $L_f(s)$ using Berndt’s method, and an estimate of zero-density of the derivatives of $L_f(s)$ based on Littlewood’s method.

Authors

  • Yoshikatsu YashiroGraduate School of Mathematics
    Nagoya University
    Nagoya 464-8602, Japan
    e-mail

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