Oscillatory properties of arithmetical functions. II
type: Item
instance of: scholarly article
title: Oscillatory properties of arithmetical functions. II
zbMATH Open document ID: 0631.10026
DOI: 10.1007/BF01951008
published in: Acta Mathematica Hungarica
publication date: 1987-01-01T00:00:00Z
review text: In the first paper in this series [ibid. 48, 173--185 (1986; Zbl 0613.10036)] the authors proved that a real-valued function \(f(x)\) has at least \(c(f) \log Y\) sign-changes in the interval \((0,Y]\) provided that the analytic continuation of its Mellin transform has all of its singularities of a certain form. The purpose of this paper is to generalize this result for a much wider class of functions. The theorem has immediate applications to the theory of distribution of prime numbers, the oscillatory properties of the difference \(\pi(x)-li(x)\), and of the similar difference for primes in an arithmetic progression.
reviewed by: W. E. Briggs
Mathematics Subject Classification ID: 11N64
Mathematics Subject Classification ID: 11N37
Mathematics Subject Classification ID: 11N05
Mathematics Subject Classification ID: 11N13
zbMATH DE Number: 4025523
zbMATH Keywords: real-valued function
zbMATH Keywords: sign-changes
zbMATH Keywords: distribution of prime numbers
zbMATH Keywords: oscillatory properties
zbMATH Keywords: arithmetic progression
author: J. Kaczorowski
author: János Pintz
MaRDI profile type: Publication
cites work: A note on the distribution of primes
cites work: On sign-changes in the remainder-term of the prime-number formula, I
cites work: Some remarks on factorization in algebraic number fields
cites work: Oscillatory properties of arithmetical functions. I
cites work: Q4402415
cites work: Q5815001
full work available at URL: https://doi.org/10.1007/bf01951008
OpenAlex ID: W2081738180
description: scientific article; zbMATH DE number 4025523