On some connections between zeta-zeros and square-free integers
type: Item
instance of: scholarly article
title: On some connections between zeta-zeros and square-free integers
zbMATH Open document ID: 0764.11039
DOI: 10.1007/BF01572078
author: Krystyna Maria Bartz
published in: Monatshefte für Mathematik
publication date: 1993-05-12T00:00:00Z
full work available at URL: https://eudml.org/doc/178571
review text: The main purpose of the paper is to present a complex explicit formula for square-free integers and an application to the proof of the classical explicit formula for the number of square-free integers not exceeding \(x\). More precisely, it is constructed and studied in detail a meromorphic function defined in terms of a certain sum involving all non- real zeros of the Riemann zeta-function. This function has simple poles with residues \(|\mu(n)|\) (\(\mu\) is the Möbius function) at all numbers \(\log n\), where \(n\) is square-free or \(n\) is equal to 1, and is regular everywhere else.
Mathematics Subject Classification ID: 11N25
Mathematics Subject Classification ID: 11M26
zbMATH DE Number: 164923
zbMATH Keywords: explicit formula for square-free integers
zbMATH Keywords: non-real zeros
zbMATH Keywords: Riemann zeta- function
zbMATH Keywords: Möbius function
MaRDI profile type: Publication
cites work: Q4149530
cites work: Q5519244
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cites work: On some complex explicit formulae connected with the Mobius function. II
OpenAlex ID: W2071713087
description: scientific article; zbMATH DE number 164923