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.
Shigeki Egami, Kohji Matsumoto
Shinjuku-ku; 1247 Yachigusa, Yakusa-cho
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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