Year: 2021
Type: preprint
Abstract: Let $ x\geq 1 $ be a large number, let $ [x]=x-\{x\} $ be the largest integer function, and let $ φ(n)$ be the Euler totient function. The asymptotic formula for the new finite sum over the primes $ \sum_{p\leq x}φ([x/p])=(6/π^2)x\log \log x+c_0x+O\left (x(\log x)^{-1}\right) $, where $c_0$ is a constant, is evaluated in this note.
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: W3176971774