对称幂 L 函数 Dirichlet 系数第二矩的渐近线

Pub Date : 2024-06-24 DOI:10.1007/s10986-024-09636-0
Xue Han, Huafeng Liu
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引用次数: 0

摘要

设 m ≥ 2 为整数。设 f 是全模态群 SL(2, ℤ) 偶数权 k 的全形赫克特征形式。用 λSymm f (n) 表示与 f 有关的相应对称幂 L 函数 L(s, Symm f) 的第 n 个归一化 Dirichlet 系数。本文将研究 Dirichlet 系数 λSymm f (n) 的第二矩的平均行为,并建立其渐近公式。
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Asymptotics for the second moment of the Dirichlet coefficients of symmetric power L-functions

Let m ≥ 2 be an integer. Let f be a holomorphic Hecke eigenform of even weight k for the full modular group SL(2, ℤ). Denote by λSymm f (n) the nth normalized Dirichlet coefficient of the corresponding symmetric power L-function L(s, Symm f) related to f. In this paper, we study the average behavior of the second moment of the Dirichlet coefficients λSymm f (n) and establish its asymptotic formula.

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