Functiones et Approximatio Commentarii Mathematici

Multiple zeros of Dedekind zeta functions

Jerzy Browkin

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It is proved that there are Dedekind's zeta functions with multiple zeros inthe critical strip of arbitrarily large multiplicity. There are given examplesof such zeros of the Dedekind zeta function of the field $\mathbb{Q}(\zeta_3, {\root 3 \of 5})$.

Article information

Funct. Approx. Comment. Math., Volume 49, Number 2 (2013), 383-390.

First available in Project Euclid: 20 December 2013

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Zentralblatt MATH identifier

Primary: 11M26: Nonreal zeros of $\zeta (s)$ and $L(s, \chi)$; Riemann and other hypotheses
Secondary: 20C15: Ordinary representations and characters

Dedekind's zeta functions Artin's $L$-functions zeros in thecritical strip induced characters


Browkin, Jerzy. Multiple zeros of Dedekind zeta functions. Funct. Approx. Comment. Math. 49 (2013), no. 2, 383--390. doi:10.7169/facm/2013.49.2.15.

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