Analytic behavior of some Euler products

Jinho Han, Haseo Ki, Donghoon Park

Research output: Contribution to journalArticlepeer-review


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

Original languageEnglish
Pages (from-to)539-548
Number of pages10
JournalRocky Mountain Journal of Mathematics
Issue number2
Publication statusPublished - 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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