算术级数上一般 L 函数的系数之和及其应用

Pub Date : 2024-07-17 DOI:10.1016/j.jnt.2024.06.011

Dan Wang

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引用次数: 0

摘要

在本文中，我们在没有拉马努扬猜想的情况下研究了算术级数上一般-函数系数的渐近分布。作为应用，我们考虑了全形形式或马斯形式在算术级数上的傅里叶系数的高均值，并改进了蒋和吕（Jiang and Lü）的结果。我们的新结果消除了对素数模块的限制，改善了模块的区间长度。

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Sums of coefficients of general L-functions over arithmetic progressions and applications

In this paper, we study the asymptotic distribution of coefficients of general L-functions over arithmetic progressions without the Ramanujan conjecture. As an application, we consider the high mean of Fourier coefficients of holomorphic forms or Maass forms for $Γ = SL (2, Z)$ over arithmetic progressions, and improve the results of Jiang and Lü [10]. Our new results remove the restriction to prime module and improve the interval length of module q.

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