Möbius function and primes: an identity factory with applications

Olivier Ramaré, Sebastian Zuniga Alterman

We investigate the sums ${\sum }_{n\le X,(n,q)=1}\frac{\hat{I}¼(n)}{n^s}{\log }^k\left(\frac{X}{n}\right)$, where $k\in \{0,1\}$, $s\in \mathbb{C}$, $\Re s>0$. Our goal is to obtain explicit as…