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On the location of the zero-free half-plane of a random Epstein zeta function

Journal article
Authors A. Strombergsson
Anders Södergren
Published in Mathematische Annalen
Volume 371
Issue 3-4
Pages 1191-1227
ISSN 0025-5831
Publication year 2018
Published at Department of Mathematical Sciences, Algebra and Geometry
Pages 1191-1227
Language en
Keywords linear-combinations, quadratic-forms, number, minima, real, Mathematics
Subject categories Mathematics


In this note we study, for a random lattice L of large dimension n, the supremum of the real parts of the zeros of the Epstein zeta function and prove that this random variable scaled by has a limit distribution, which we give explicitly. This limit distribution is studied in some detail; in particular we give an explicit formula for its distribution function. Furthermore, we obtain a limit distribution for the frequency of zeros of in vertical strips contained in the half-plane n/2.

Page Manager: Webmaster|Last update: 9/11/2012

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