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

2023/02/06 by Shigeki Egami, Egami, Shigeki, Kohji Matsumoto +1
Mathematics · #11M06 #11M26 #11M41 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2302.02549

openalex publication_date 2023/02/06 · openalex created_date 2023/02/09 · openalex updated_date 2026/07/28

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.

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