Sur la somme de M\"obius $\sum_{n \leqslant x} \mu(n)n^{-s}$ autour de $s=1$ et des sommes d\'eriv\'ees, premi\`ere \'etude

TL;DR

This paper explicitly analyzes the partial sums of the inverse of the Riemann zeta function and its derivative around s=1, providing new insights into their behavior and sums.

Contribution

It offers a novel explicit study of the partial sums of the Möbius function's sum and derivatives near s=1, advancing understanding of these sums.

Findings

Explicit formulas for partial sums near s=1

Insights into the behavior of the Möbius function sums

Analysis of derivatives related to the zeta function

Abstract

We study in an explicit manner the partial sums of the multiplicative inverse of the Riemann zeta function and its derivative.