Irregularities in the distribution of primes in arithmetic progressions. II
type: Item
instance of: scholarly article
title: Irregularities in the distribution of primes in arithmetic progressions. II
zbMATH Open document ID: 0558.10037
DOI: 10.1007/BF01196659
author: S. Salerno
author: János Pintz
published in: Archiv der Mathematik
publication date: 1984-01-01T00:00:00Z
review text: With the same finite Riemann-Piltz assumption as in part I (see the preceding review), the authors extend those results by obtaining lower bounds for various definite integrals of \(| \Delta_ i(x)|\), \(i=1,2,3,4\), where the meaning for \(i=2,4\) is given in the review of part I. \(\Delta_ 1(x)=\sum_{p\leq x, p\equiv \ell_ 1 (q)}1-\sum_{p\leq x, p\equiv \ell_ 2 (q)}1\) and \(\Delta_ 3(x)\) is the same difference with summands log p.
Mathematics Subject Classification ID: 11N37
Mathematics Subject Classification ID: 11N13
zbMATH DE Number: 3889652
zbMATH Keywords: oscillatory properties
zbMATH Keywords: lower bounds
zbMATH Keywords: mean value
reviewed by: W. E. Briggs
MaRDI profile type: Publication
cites work: Contributions to the theory of the distribution of prime numbers in arithmetical progressions I
cites work: Irregularities in the distribution of primes in arithmetic progressions. I
full work available at URL: https://doi.org/10.1007/bf01196659
OpenAlex ID: W2010552964
description: scientific article; zbMATH DE number 3889652