Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2024; 61(1): 135-145

Online first article January 23, 2024      Printed January 31, 2024

https://doi.org/10.4134/BKMS.b230063

Copyright © The Korean Mathematical Society.

A function-field analogue of the Goldbach counting function and the associated Dirichlet series

Shigeki Egami, Kohji Matsumoto

Shinjuku-ku; 1247 Yachigusa, Yakusa-cho

Abstract

We consider a function-field analogue of Dirichlet series associated with the Goldbach counting function, and prove that it can, or cannot, be continued meromorphically to the whole plane. When it cannot, we further prove the existence of the natural boundary of it.

Keywords: Goldbach counting function, function field, von Mangoldt function, meromorphic continuation, natural boundary

MSC numbers: Primary 111M41; Secondry 11M06, 11M26

Supported by: The second named author was supported by Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research No.22K03267.

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