Values of zeta-one functions at positive even integers

Masato Kobayashi; Shunji Sasaki

Values of zeta-one functions at positive even integers

Number Theory 2022-03-10 v2

Authors: Masato Kobayashi , Shunji Sasaki

Abstract

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.

Keywords

zeta-one functions riemann zeta function positive even integers residue theorem infinite sums

Cite

@article{arxiv.2202.11835,
  title  = {Values of zeta-one functions at positive even integers},
  author = {Masato Kobayashi and Shunji Sasaki},
  journal= {arXiv preprint arXiv:2202.11835},
  year   = {2022}
}

Comments

12 pages. Version 2: fixed the proof of Theorem 1.3

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