Analytic behavior of some Euler products

Jinho Han; Haseo Ki; Donghoon Park

doi:10.1216/RMJ.2021.51.539

Analytic behavior of some Euler products

Jinho Han, Haseo Ki, Donghoon Park

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We investigate analytic properties for some Euler products. In particular, we construct an Euler product Π_p:prime(1-α_pp^-s)^-1(|α_p| = 1 for any prime number p) with natural boundary on Re(s) = 1.

Original language	English
Pages (from-to)	539-548
Number of pages	10
Journal	Rocky Mountain Journal of Mathematics
Volume	51
Issue number	2
DOIs	https://doi.org/10.1216/RMJ.2021.51.539
Publication status	Published - 2021 Apr

Bibliographical note

Funding Information:
This work was supported by a National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIP) (No. 2017R1A2B2002702). 2010 AMS Mathematics subject classification: primary 11M41; secondary 11M26. Keywords and phrases: Euler products, natural boundaries. Received by the editors on July 1, 2019, and in revised form on September 28, 2020.

Publisher Copyright:
© 2021 Rocky Mountain Mathematics Consortium. All rights reserved.

All Science Journal Classification (ASJC) codes

Mathematics(all)

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10.1216/RMJ.2021.51.539

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author = "Jinho Han and Haseo Ki and Donghoon Park",

note = "Funding Information: This work was supported by a National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIP) (No. 2017R1A2B2002702). 2010 AMS Mathematics subject classification: primary 11M41; secondary 11M26. Keywords and phrases: Euler products, natural boundaries. Received by the editors on July 1, 2019, and in revised form on September 28, 2020. Publisher Copyright: {\textcopyright} 2021 Rocky Mountain Mathematics Consortium. All rights reserved.",

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Analytic behavior of some Euler products

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

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