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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
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].
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- Copyright © University College London 2019
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