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arXiv · 2410.00329

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

Zhen Guo·Xin Li
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Abstract

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

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Zhen Guo, Xin Li. 2024-10-01. On a sum of the error term of the Dirichlet divisor function over primes. https://arxiv.org/abs/2410.00329

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