Functiones et Approximatio Commentarii Mathematici

Multiple zeros of Dedekind zeta functions

Jerzy Browkin

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Abstract

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

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

Dates
First available in Project Euclid: 20 December 2013

Permanent link to this document
https://projecteuclid.org/euclid.facm/1387572240

Digital Object Identifier
doi:10.7169/facm/2013.49.2.15

Mathematical Reviews number (MathSciNet)
MR3161504

Zentralblatt MATH identifier
1283.11119

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

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

Citation

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. https://projecteuclid.org/euclid.facm/1387572240


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References

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