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Superposition of zeros of distinct L-functions
Journal article   Peer reviewed

Superposition of zeros of distinct L-functions

Jianya Liu and Yangbo Ye
Forum mathematicum, Vol.14(3), pp.419-455
2002
DOI: 10.1515/form.2002.020

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Abstract

In this paper we first prove a weighted prime number theorem of an ''o¤-diagonal'' type for Rankin-Selberg L-functions of automorphic representations of GLm and GLm0 over Q. Then for ma 1, or under the Selberg orthonormality conjecture for mV 2, we prove that non- trivial zeros of distinct primitive automorphic L-functions for GLm over Q are uncorrelated, for certain test functions whose Fourier transforms have restricted support. For the same test functions, we also prove that the n-level correlation of non-trivial zeros of a product of such L-functions follows the distribution of the superposition of GUE models for individual L-functions and GUEs of lower ranks.

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