On the series expansion of a square-free zeta series

2023/12/28 by Kawalec, Artur
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2312.16811

Abstract

In this article, we develop a square-free zeta series associated with the Möbius function into a power series, and prove a Stieltjes like formula for these expansion coefficients. We also investigate another analytical continuation of these series and develop a formula for ζ(\tfrac12) in terms of the Möbius function, and in the last part, we explore an alternating series version of these results.

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