A comparison of zeros of \(L\)-functions
type: Item
instance of: scholarly article
title: A comparison of zeros of \(L\)-functions
zbMATH Open document ID: 0978.11045
author: Ravi Raghunathan
published in: Mathematical Research Letters
publication date: 2000-08-13T00:00:00Z
review text: Let \(L(s) = L_1(s)/L_2(s)\) be the quotient of two automorphic \(L\)-functions for some \(\text{GL}(n)\) over a number field. The author proves in several cases that \(L(s)\) has infinitely many non-trivial poles. For the quotient of two Dirichlet \(L\)-functions for \({\mathbb Q}\) (automorphic \(L\)-functions for \(\text{GL}(1)\)) a proof is given by a simple trick using the converse theorem for \(\text{GL}(1)\) over \({\mathbb Q}\). Other examples use an extension of Hecke's converse theorem for \(\text{GL}(2)\) over \({\mathbb Q}\) proved by the author. The knowledge of analytic properties of the automorphic \(L\)-functions in question is necessary for application of the method.
Mathematics Subject Classification ID: 11M26
Mathematics Subject Classification ID: 11F66
Mathematics Subject Classification ID: 11R42
zbMATH DE Number: 1489492
zbMATH Keywords: automorphic \(L\)-functions
zbMATH Keywords: poles
reviewed by: J. G. M. Mars
MaRDI profile type: Publication
DOI: 10.4310/MRL.1999.V6.N2.A4
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description: scientific article; zbMATH DE number 1489492