Mean-square estimate of automorphic <i>L</i>-functions

Weili YAO

doi:10.1007/s11464-020-0817-1

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Front. Math. China ›› 2020, Vol. 15 ›› Issue (1) : 205-213. DOI: 10.1007/s11464-020-0817-1

RESEARCH ARTICLE

Mean-square estimate of automorphic L-functions

Weili YAO

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Abstract

Let f be a holomorphic Hecke cusp form with even integral weight $k ≥ 2$ for the full modular group, and let $χ$ be a primitive Dirichlet character modulo q. Let $L f (s, χ)$ be the automorphic L-function attached to f and $χ$ . We study the mean-square estimate of $L f (s, χ)$ and establish an asymptotic formula.

Keywords

Automorphic L-function / cusp form / Fourier coe_cient

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Weili YAO. Mean-square estimate of automorphic L-functions. Front. Math. China, 2020, 15(1): 205‒213 https://doi.org/10.1007/s11464-020-0817-1

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