Functiones et Approximatio Commentarii Mathematici

Simple zeros of Dedekind zeta functions

Stéphane R. Louboutin

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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.

Article information

Source
Funct. Approx. Comment. Math., Volume 56, Number 1 (2017), 109-116.

Dates
First available in Project Euclid: 27 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.facm/1485486021

Digital Object Identifier
doi:10.7169/facm/1598

Mathematical Reviews number (MathSciNet)
MR3629014

Zentralblatt MATH identifier
06864149

Subjects
Primary: 11R42: Zeta functions and $L$-functions of number fields [See also 11M41, 19F27]
Secondary: 11R29: Class numbers, class groups, discriminants

Keywords
Dedekind zeta function Siegel zero

Citation

Louboutin, Stéphane R. Simple zeros of Dedekind zeta functions. Funct. Approx. Comment. Math. 56 (2017), no. 1, 109--116. doi:10.7169/facm/1598. https://projecteuclid.org/euclid.facm/1485486021


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