对称幂 L 函数 Dirichlet 系数第二矩的渐近线

IF 0.5 4区 数学 Q3 MATHEMATICS
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。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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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来源期刊
CiteScore
0.90
自引率
0.00%
发文量
33
审稿时长
>12 weeks
期刊介绍: The Lithuanian Mathematical Journal publishes high-quality original papers mainly in pure mathematics. This multidisciplinary quarterly provides mathematicians and researchers in other areas of science with a peer-reviewed forum for the exchange of vital ideas in the field of mathematics. The scope of the journal includes but is not limited to: Probability theory and statistics; Differential equations (theory and numerical methods); Number theory; Financial and actuarial mathematics, econometrics.
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