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March 2017 Simple zeros of Dedekind zeta functions
Stéphane R. Louboutin
Funct. Approx. Comment. Math. 56(1): 109-116 (March 2017). DOI: 10.7169/facm/1598

Abstract

Using Stechkin's lemma we derive explicit regions of the half complex plane $\Re (s)\leq 1$ in which the Dedekind zeta function of a number field $K$ has at most one complex zero, this zero being real if it exists. These regions are Stark-like regions, i.e. given by all $s=\beta +i\gamma$ with $\beta\geq 1-c/\log d_K$ and $\vert\gamma\vert\leq d/\log d_K$ for some absolute positive constants $c$ and $d$. These regions are larger and our proof is simpler than recently published such regions and proofs.

Citation

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Stéphane R. Louboutin. "Simple zeros of Dedekind zeta functions." Funct. Approx. Comment. Math. 56 (1) 109 - 116, March 2017. https://doi.org/10.7169/facm/1598

Information

Published: March 2017
First available in Project Euclid: 27 January 2017

zbMATH: 06864149
MathSciNet: MR3629014
Digital Object Identifier: 10.7169/facm/1598

Subjects:
Primary: 11R42
Secondary: 11R29

Rights: Copyright © 2017 Adam Mickiewicz University

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Vol.56 • No. 1 • March 2017
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