On Second Moment of Selberg Zeta-Function for σ=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma =1$$\end{document}

被引：0
作者：
Paulius Drungilas
Ramūnas Garunkštis
Aivaras Novikas
机构：
[1] Vilnius University,Institute of Mathematics, Faculty of Mathematics and Informatics
来源：
Results in Mathematics | 2021年 / 76卷 / 4期
关键词：
Selberg zeta-function; second moment; mean value theorems; Beurling zeta-function; 11M26; 11M36; 11M41;
D O I：
10.1007/s00025-021-01492-5
中图分类号：
学科分类号：
摘要：
Let Z(s) be the Selberg zeta-function for the modular group. We consider the existence of the second moments of Z(s) and of its reciprocal on σ=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma =1$$\end{document}. The existence of such moments is related to the properties of certain Beurling natural numbers. Here the behavior of the counting function and the distribution of minimal gaps between these Beurling natural numbers are important. We also obtain unconditional upper bounds for these moments.
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