On the zeros of linear combinations of the Matsumoto zeta-functions
type: Item
instance of: scholarly article
title: On the zeros of linear combinations of the Matsumoto zeta-functions
zbMATH Open document ID: 0922.11074
DOI: 10.1007/BF02465551
published in: Lithuanian Mathematical Journal
publication date: 1999-03-15T00:00:00Z
review text: Let \(\phi_1(s),\dots, \phi_r(s)\) be Matsumoto zeta-functions, defined by generalized Euler products, and satisfying appropriate regularity conditions. Let \(V(s)\) be a non-trivial linear combination of \(\phi_1(s),\dots, \phi_r(s)\), and suppose that they are independent in a suitable sense. Then it is shown that \(V(s)\) has \(\gg T\) zeros in the region \(\sigma_1\leq\sigma\leq \sigma_2\), \(0\leq t\leq T\), for any \(\sigma_1<\sigma_2\) in the right-hand half of the critical strip. The proof is based on a multidimensional limit theorem for the distribution of the functions \(\phi_1(s),\dots, \phi_r(s)\), which produces regions in which \(V(s)\) approximates any desired analytic function.
reviewed by: D. R. Heath-Brown
Mathematics Subject Classification ID: 11M41
Mathematics Subject Classification ID: 11M26
zbMATH DE Number: 1262940
zbMATH Keywords: approximation of analytic function
zbMATH Keywords: Matsumoto zeta-functions
zbMATH Keywords: generalized Euler products
zbMATH Keywords: zeros
zbMATH Keywords: critical strip
zbMATH Keywords: multidimensional limit theorem
zbMATH Keywords: distribution of the functions
author: Antanas Laurinčikas
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1262940