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.
Bibliographical noteFunding 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.
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