Year: 2021
Type: preprint
Abstract: Let $ x\geq 1 $ be a large number, let $ [x]=x-\{x\} $ be the largest integer function, and let $ σ(n)$ be the sum of divisors function. This note presents the first proof of the asymptotic formula for the average order $ \sum_{p\leq x}σ([x/p])=c_0x\log \log x+O(x) $ over the primes, where $c_0>0$ is a constant. More generally, $ \sum_{p\leq x}σ([x/(p+a)])=c_0x\log \log x+O(x) $ for any fixed integer $a$.
Source: arXiv (Cornell University)
Author: Carella, N. A.
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3181032815