Truncated convolution of the Möbius function and multiplicative energy of an integer $n$
Volume 195 / 2020
Acta Arithmetica 195 (2020), 83-95
MSC: 11N37, 11N56, 11N64.
DOI: 10.4064/aa190515-18-10
Published online: 15 April 2020
Abstract
We establish an interesting upper bound for the moments of a truncated Dirichlet convolution of the Möbius function, denoted $M(n,z)$. Our result implies that $M(n,j)$ is usually quite small for $j \in \{1,\dots ,n\}$. Also, we establish an estimate for the multiplicative energy of the set of divisors of an integer $n$.
