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ON SIMPLE ZEROS OF THE DEDEKIND ZETA-FUNCTION OF A QUADRATIC NUMBER FIELD

Published online by Cambridge University Press:  22 May 2019

Xiaosheng Wu
Affiliation:
School of Mathematics, Hefei University of Technology, Hefei 230009, China email [email protected]
Lilu Zhao
Affiliation:
School of Mathematics, Shandong University, Jinan 250100, China email [email protected]
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Abstract

We study the number of non-trivial simple zeros of the Dedekind zeta-function of a quadratic number field in the rectangle $\{\unicode[STIX]{x1D70E}+\text{i}t:0<\unicode[STIX]{x1D70E}<1,0<t<T\}$. We prove that such a number exceeds $T^{6/7-\unicode[STIX]{x1D700}}$ if $T$ is sufficiently large. This improves upon the classical lower bound $T^{6/11}$ established by Conrey et al [Simple zeros of the zeta function of a quadratic number field. I. Invent. Math.86 (1986), 563–576].

Type
Research Article
Copyright
Copyright © University College London 2019 

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