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arXiv · 1402.3716

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

Yoshikatsu Yashiro
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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 $L_f(s)$.

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Yoshikatsu Yashiro. 2014-02-15. Approximate functional equation and mean value formula for the derivatives of $L$-functions attached to cusp forms. https://arxiv.org/abs/1402.3716

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