A Bohr-Jessen type theorem for the Epstein zeta-function
type: Item
instance of: scholarly article
title: A Bohr-Jessen type theorem for the Epstein zeta-function
zbMATH Open document ID: 1410.11111
author: Antanas Laurinčikas
author: Renata Macaitienė
published in: Results in Mathematics
publication date: 2018-12-18T00:00:00Z
review text: It is known that the Epstein zeta-function \(\zeta (s;Q),s=\sigma +it\), is defined for \(\sigma >n/2\) by the series \[ \zeta (s;Q)=\sum_{\underline{x}\in \mathbb{Z}^{n}-\{0\}}\frac{1}{(Q[\underline{x}])^{s}}, \] where \(Q\) is a positive definite quadratic \(n\times n\) matrix and \(Q[\underline{x}])=\underline{x}^{T}Q\underline{x}\), and is meromorphically continued to the whole complex plane. In this paper, the authors consider a Bohr-Jessen type theorem for the Epstein zeta-function \(\zeta (s;Q)\) and prove that for \(\sigma >(n-1)/2,T\rightarrow \infty \), a limit theorem on the weak convergence of \[ \frac{1}{T}\text{meas}\{t\in [ 0,T]:\zeta (\sigma +it;Q)\in A\}, \] where \(A\in \mathcal{B}(\mathbb{C})\).
reviewed by: Ahmet Tekcan
Mathematics Subject Classification ID: 11M41
Mathematics Subject Classification ID: 11E45
Mathematics Subject Classification ID: 11M06
zbMATH DE Number: 6995204
zbMATH Keywords: Epstein zeta-function
zbMATH Keywords: limit theorem
zbMATH Keywords: Haar measure
zbMATH Keywords: weak convergence
MaRDI profile type: Publication
full work available at URL: s00025-018-0909-3
OpenAlex ID: W4232429389
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DOI: 10.1007/S00025-018-0909-3
description: scientific article; zbMATH DE number 6995204