Values of zeta-one functions at positive even integers

Abstract

Motivated by Euler-Goldbach and Shallit-Zikan theorems, we introduce zeta-one functions with infinite sums of $n^s\pm 1$ as an analogy of the Riemann zeta function. Then we compute values of these functions at positive even integers by the residue theorem.

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