与西格尔顶点形式相关的朗伯数列的渐近展开

Babita, Abhash Kumar Jha, Abhishek Juyal, Bibekananda Maji
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引用次数: 0

摘要

2000 年,Hafner 和 Stopple 证明了 Zagier 的一个猜想,即自变函数 \(|\Delta (x+iy)|^2\) 的常数项,即 Lambert 数列 \(\sum _{n=1}^\infty \tau (n)^2 e^{-4 \pi n y}/),可以用黎曼zeta函数的非琐零点来表示。在本文中,我们将研究与西格尔尖顶形式相关的上述兰伯特级数的广义版本的渐近展开。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
An asymptotic expansion for a Lambert series associated with Siegel cusp forms

In 2000, Hafner and Stopple proved a conjecture of Zagier which states that the constant term of the automorphic function \(|\Delta (x+iy)|^2\), i.e., the Lambert series \(\sum _{n=1}^\infty \tau (n)^2 e^{-4 \pi n y}\), can be expressed in terms of the non-trivial zeros of the Riemann zeta function. In this article, we study an asymptotic expansion of a generalized version of the aforementioned Lambert series associated with Siegel cusp forms.

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