Distribution of zeros and zero-density estimates for the derivatives of $L$-functions attached to cusp forms

Yoshikatsu Yashiro

Distribution of zeros and zero-density estimates for the derivatives of $L$-functions attached to cusp forms

Number Theory 2014-07-04 v2

Authors: Yoshikatsu Yashiro

Abstract

Let $f$ be a holomorphic cusp form of weight $k$ with respect to $SL_2(\mathbb{Z})$ which is a normalized Hecke eigenform, $L_f(s)$ the $L$ -function attached to the form $f$ . In this paper, we shall give the relation of the number of zeros of $L_f(s)$ and 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.

Keywords

$L$-functions cusp forms zero-density estimates derivatives Hecke eigenforms Berndt's method Littlewood's method

Cite

@article{arxiv.1402.3800,
  title  = {Distribution of zeros and zero-density estimates for the derivatives of $L$-functions attached to cusp forms},
  author = {Yoshikatsu Yashiro},
  journal= {arXiv preprint arXiv:1402.3800},
  year   = {2014}
}

Comments

21 pages

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