A note on a result of Bochner and Conrey-Ghosh about the Selberg class
type: Item
instance of: scholarly article
title: A note on a result of Bochner and Conrey-Ghosh about the Selberg class
zbMATH Open document ID: 0926.11062
published in: Archiv der Mathematik
publication date: 1999-07-20T00:00:00Z
review text: It is well known [see \textit{S. Bochner}, Ann. Math. (2) 67, 29-41 (1958; Zbl 0082.29002) and \textit{J. B. Conrey} and \textit{A. Ghosh}, Duke Math. J. 72, 673-693 (1993; Zbl 0796.11037)], that there are no functions of degree \(0< d<1\) in the Selberg class of Dirichlet series with functional equation and Euler product. The author gives two simple proofs of this result. The first is based on the classical formula for the \(n\)-th coefficients of Dirichlet series; the second is based on Perron's formula. We remark that Molteni's first proof was already given by \textit{H.-E. Richert} [Acad. Serbe Sci., Publ. Inst. Mat. 11, 73-124 (1957; Zbl 0082.05802)], who apparently first proved the above result.
reviewed by: A. Perelli
Mathematics Subject Classification ID: 11M41
Mathematics Subject Classification ID: 11M99
zbMATH DE Number: 1295494
zbMATH Keywords: zeta-functions
zbMATH Keywords: Selberg class
zbMATH Keywords: Dirichlet series with functional equation
zbMATH Keywords: Perron's formula
author: Giuseppe Molteni
MaRDI profile type: Publication
full work available at URL: s000130050325
OpenAlex ID: W2026505068
DOI: 10.1007/S000130050325
description: scientific article; zbMATH DE number 1295494