Analytic behavior of some Euler products

Jinho Han; Haseo Ki; Donghoon Park

doi:10.1216/rmj-2021-51-539

Abstract

We investigate analytic properties for some Euler products. In particular, we construct an Euler product ${\prod _{p:{\rm{\;prime}}}}{\left( {1 - {\alpha _p}{p^{ - s}}} \right)^{ - 1}}$ $\left( {\left| {{\alpha _p}} \right| = 1{\rm{\;\;for\;any\;prime\;number\;}}p} \right)$ with natural boundary on ${\rm{\;Re}}\left( s \right) = 1$ .

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Jinho Han. Haseo Ki. Donghoon Park. "Analytic behavior of some Euler products." Rocky Mountain J. Math. 51 (2) 539 - 548, April 2021. https://doi.org/10.1216/rmj.2021.51.539

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Received: 1 July 2019; Revised: 28 September 2020; Accepted: 1 October 2020; Published: April 2021

First available in Project Euclid: 25 June 2021

Digital Object Identifier: 10.1216/rmj.2021.51.539

Subjects:

Primary: 11M41

Secondary: 11M26

Keywords: Euler products , natural boundaries

Abstract

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