Möbius function and primes: an identity factory with applications

We investigate the sums $\sum_{n\le X, (n,q)=1}\frac{μ(n)}{n^s}\log^k\left(\frac{X}{n}\right)$, where $k\in\{0,1\}$, $s\in\mathbb{C}$, $\Re s>0$. Our goal is to obtain explicit asymptotic estimations for these quantities. To achieve this, we develop a broad framework of identities that we use to derive several applications. Building on similar principles, we also provide an appendix establishing the inequality $\sum_{n\le X}Λ(n)/n\le \log X$, valid for any $X\geq 1$.

No reviews yet.

No comments yet.