Values of zeta-one functions at positive even integers

Motivated by Euler-Goldbach and Shallit-Zikan theorems, we introduce zeta-one functions with infinite sums of $n^{s}\pm1$ as an analogy of the Riemann zeta function. Then we compute values of these functions at positive even integers by the residue theorem.

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Veröffentlicht in:	arXiv.org 2022-03
Hauptverfasser:	Kobayashi, Masato, Sasaki, Shunji
Format:	Artikel
Sprache:	eng
Schlagworte:	Integers Theorems
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creator	Kobayashi, Masato Sasaki, Shunji
description	Motivated by Euler-Goldbach and Shallit-Zikan theorems, we introduce zeta-one functions with infinite sums of $n^{s}\pm1$ as an analogy of the Riemann zeta function. Then we compute values of these functions at positive even integers by the residue theorem.
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title	Values of zeta-one functions at positive even integers
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