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ONE-LEVEL DENSITY OF LOW-LYING ZEROS OF QUADRATIC HECKE L-FUNCTIONS OF IMAGINARY QUADRATIC NUMBER FIELDS

Published online by Cambridge University Press:  29 October 2020

PENG GAO
Affiliation:
School of Mathematical Sciences, Beihang University, Beijing 100191, China e-mail: penggao@buaa.edu.cn
LIANGYI ZHAO
Affiliation:
School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia
Corresponding

Abstract

In this paper, we prove a one level density result for the low-lying zeros of quadratic Hecke L-functions of imaginary quadratic number fields of class number 1. As a corollary, we deduce, essentially, that at least $(19-\cot (1/4))/16 = 94.27\ldots \%$ of the L-functions under consideration do not vanish at 1/2.

Type
Research Article
Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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Footnotes

Communicated by Michael Coons

The first-named author was supported in part by NSFC grant 11871082 and the second-named author by the FRG grant PS43707 at UNSW.

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ONE-LEVEL DENSITY OF LOW-LYING ZEROS OF QUADRATIC HECKE L-FUNCTIONS OF IMAGINARY QUADRATIC NUMBER FIELDS
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