A number theoretic series of I. Kasara
type: Item
instance of: scholarly article
title: A number theoretic series of I. Kasara
zbMATH Open document ID: 0505.10024
author: Harold G. Diamond
published in: Pacific Journal of Mathematics
publication date: 1984-01-01T00:00:00Z
review text: \textit{I. Kasara} [Tr. Samark. Gos. Univ. Im. Alishera Navoi, Nov. Ser. 235, 64--66 (1973; Zbl 0541.10041)] considered the series \[ S(x) = 1+\sum_{k\geq 1}\frac{1}{k!}\sum_{n_ 1,\ldots,n_ k\leq x,n_ i>1}\frac{1}{\log n_ 1 \dots \log n_ k}, \] and he asserted that \(S(x) = x+O(x/\log x)\). In this note the author shows that this assertion is not correct. He proves with the aid of one of his theorems concerning Beurling generalized primes that \[ S(x) = c x+O(x\,\exp (-(\log x)^{1/2-\varepsilon})) \] with a constant \(c>1\).
reviewed by: Helmut Müller
Mathematics Subject Classification ID: 11M99
Mathematics Subject Classification ID: 11N80
zbMATH DE Number: 3796052
zbMATH Keywords: Beurling generalized prime numbers
MaRDI profile type: Publication
full work available at URL: pjm.1984.111.283
OpenAlex ID: W2039579193
DOI: 10.2140/PJM.1984.111.283
description: scientific article; zbMATH DE number 3796052