English

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

Number Theory 2023-02-07 v1

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

Cite

@article{arxiv.2302.02549,
  title  = {A function-field analogue of the Goldbach counting function and the associated Dirichlet series},
  author = {Shigeki Egami and Kohji Matsumoto},
  journal= {arXiv preprint arXiv:2302.02549},
  year   = {2023}
}

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10pages