On the location of the zero-free half-plane of a random Epstein zeta function
Journal article, 2018

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 En(L, s) and prove that this random variable scaled by n- 1has 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 En(L, s) in vertical strips contained in the half-plane Rs>n2.

Author

Andreas Strömbergsson

Uppsala University

Anders Södergren

Institute for Advanced Studies

Chalmers, Mathematical Sciences, Algebra and geometry

Mathematische Annalen

0025-5831 (ISSN) 1432-1807 (eISSN)

Vol. 371 3-4 1191-1227

Subject Categories

Geometry

Probability Theory and Statistics

Mathematical Analysis

DOI

10.1007/s00208-017-1589-0

More information

Latest update

9/4/2018 2