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arXiv · 2302.02549

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

Shigeki Egami·Kohji Matsumoto
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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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Shigeki Egami, Kohji Matsumoto. 2023-02-06. A function-field analogue of the Goldbach counting function and the associated Dirichlet series. https://arxiv.org/abs/2302.02549

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