2019/01/18 by Victor Volfson, Volfson, Victor Leonidovich
Mathematics · Physics and Astronomy · #11N37 #Advanced Mathematical Theories #Advanced Mathematical Theories and Applications #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1901.06160
openalex publication_date 2019/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The paper compares the asymptotic of the expressions \frac 1 x ∑n ≤ x f(n) and ∑n ≤ x \frac f(n) n, \frac 1 x ∑p ≤ x f(p) and ∑p ≤ x \frac f(p) p. The asymptotic of sums ∑n ≤ x \frac f(n) n and ∑p ≤ x \frac f(p) p (n,p - respectively, positive and prime numbers) are determined if the asymptotic of sums are known, respectively: ∑n ≤ x f(n),∑p ≤ x f(p).