Functiones et Approximatio Commentarii Mathematici

Simple zeros of Dedekind zeta functions

Stéphane R. Louboutin

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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

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

First available in Project Euclid: 27 January 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Dedekind zeta function Siegel zero


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

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