Oscillatory properties of arithmetical functions. I
type: Item
instance of: scholarly article
title: Oscillatory properties of arithmetical functions. I
zbMATH Open document ID: 0613.10036
DOI: 10.1007/BF01949062
published in: Acta Mathematica Hungarica
publication date: 1986-01-01T00:00:00Z
review text: The authors investigate the function V(f,Y), the number of sign changes of f(x) in the interval (0,Y) where certain conditions are imposed on f. Results about V(f,y) have been obtained by Landau, Polya, and Grosswald. The purpose of this paper is to prove a counterpart result to the theorem of Grosswald in which lim sup is replaced by lim inf. A corollary of the result is sharpening of Polya's theorem which can be applied to the partial sums of many number-theoretic functions.
reviewed by: W. E. Briggs
Mathematics Subject Classification ID: 11N37
zbMATH DE Number: 3991610
zbMATH Keywords: partial sums of arithmetical functions
zbMATH Keywords: sign changes
author: J. Kaczorowski
author: János Pintz
MaRDI profile type: Publication
cites work: On the Zeros of the Riemann Zeta Function in the Critical Strip. II
cites work: Q5511432
cites work: On some generalizations of theorems by Landau and Polya
cites work: Oscillation Theorems of Arithmetical Functions
cites work: Q4353516
cites work: Q3922750
cites work: Calculation of Dirichlet L-Functions
full work available at URL: https://doi.org/10.1007/bf01949062
OpenAlex ID: W4252846784
description: scientific article; zbMATH DE number 3991610