关于扩展Selberg类中阶$1$函数的线性扭曲

Pub Date : 2019-03-14 DOI:10.7169/facm/1801

Giamila Zaghloul

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引用次数: 1

摘要

给定一个1次函数$F\in\mathcal{S}^{\sharp}$和一个实数$\alpha$，我们考虑线性扭曲$F(S，\alpha)$，证明它满足一个反映$ S $为$1- S $的泛函方程，这可以看作是一个Hurwitz-Lerch型泛函方程。我们还得到了关于线性扭转的零点分布的一些结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On the linear twist of degree $1$ functions in the extended Selberg class

Given a degree 1 function $F\in\mathcal{S}^{\sharp}$ and a real number $\alpha$, we consider the linear twist $F(s,\alpha)$, proving that it satisfies a functional equation reflecting $s$ into $1-s$, which can be seen as a Hurwitz-Lerch type of functional equation. We also derive some results on the distribution of the zeros of the linear twist.

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