Helson zeta functions for characters with finitely many values

We show that the analytic continuations of Helson zeta functions ζχ(s)=∑1∞χ(n)n−s$ \zeta _\chi (s)= \sum _1^{\infty }\chi (n)n^{-s}$ can have essentially arbitrary poles and zeroes in the strip 21/40

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Bibliographic Details
Published in:The Bulletin of the London Mathematical Society 2023-10, Vol.55 (5), p.2233-2241
Main Author: Bochkov, I.
Format: Article
Language:English
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Summary:We show that the analytic continuations of Helson zeta functions ζχ(s)=∑1∞χ(n)n−s$ \zeta _\chi (s)= \sum _1^{\infty }\chi (n)n^{-s}$ can have essentially arbitrary poles and zeroes in the strip 21/40
ISSN:0024-6093
1469-2120
DOI:10.1112/blms.12847