On a sum of the error term of the Dirichlet divisor function over primes

Abstract

Let $d(n)$ be the Dirichlet divisor function and $\Delta (x)$ denote the error term of the sum ${\sum }_{n⩽x}d(n)$ for a large real variable $x$. In this paper we focus on the sum ${\sum }_{p⩽x}{\Delta }^2(p)$, where $p$ runs over primes. We prove that there exists an asymptotic formula.

arXiv comment13 pages