Approximate functional equation and mean value formula for the derivatives of $L$-functions attached to cusp forms

Yoshikatsu Yashiro

Approximate functional equation and mean value formula for the derivatives of $L$-functions attached to cusp forms

Number Theory 2015-01-20 v4

Authors: Yoshikatsu Yashiro

Abstract

Let $f$ be a holomorphic cusp form of weight $k$ with respect to full modular group $SL_2(\mathbb{Z})$ satisfying a normalized Hecke eigenform, $L_f(s)$ the $L$ -function attached to the form $f$ . Good gave the approximate functional equation and mean square formula of $L_f(s)$ . In this paper, we shall generalize these formulas for the derivatives of $L_f(s)$ .

Keywords

approximate functional equation mean value formula derivatives of l-functions cusp forms hecke eigenforms modular group analytic number theory

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@article{arxiv.1402.3716,
  title  = {Approximate functional equation and mean value formula for the derivatives of $L$-functions attached to cusp forms},
  author = {Yoshikatsu Yashiro},
  journal= {arXiv preprint arXiv:1402.3716},
  year   = {2015}
}

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32 pages

Approximate functional equation and mean value formula for the derivatives of $L$-functions attached to cusp forms

Abstract

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Cite

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