Year: 2026
Type: preprint
Abstract: Let $d(n)$ be the divisor function and denote by $[t]$ the integral part of the real number $t$. We prove that \begin{align*} \sum_{n\leq x^{1/c}}d\left(\left[\frac{x}{n^c}\right]\right)=d_cx^{1/c}+O_{\varepsilon,c}(x^{θ_c+\varepsilon}), \end{align*} where $d_c$ is a suitable constant, $θ_c<2/(3c+2)$ for $0
Source: arXiv (Cornell University)
Author: Yang, Zhiyuan
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220737741