A FUNCTION-FIELD ANALOGUE OF THE GOLDBACH COUNTING FUNCTION AND THE ASSOCIATED DIRICHLET SERIES

A FUNCTION-FIELD ANALOGUE OF THE GOLDBACH COUNTING FUNCTION AND THE ASSOCIATED DIRICHLET SERIES

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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Veröffentlicht in:Taehan Suhakhoe hoebo 2024, Vol.61 (1), p.135-145
Hauptverfasser: Shigeki Egami, Kohji Matsumoto
Format: Artikel
Sprache:kor
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Zusammenfassung: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.
ISSN:1015-8634