The critical strips of the sums \(1+2^{z}+\cdots +n^{z}\)
type: Item
instance of: scholarly article
title: The critical strips of the sums \(1+2^{z}+\cdots +n^{z}\)
zbMATH Open document ID: 1213.30002
DOI: 10.1155/2011/909674
author: J. M. Sepulcre
author: G. Mora
published in: Abstract and Applied Analysis
publication date: 2011-05-16T00:00:00Z
review text: Summary: We give a partition of the critical strip, associated with each partial sum \(1 + 2^z + \dots + n^z\) of the Riemann zeta function for \(\text{Re\,}z < - 1\), formed by infinitely many rectangles for which a formula allows us to count the number of its zeros inside each of them with an error, at most, of two zeros. A generalization of this formula is also given to a large class of almost-periodic functions with bounded spectrum.
Mathematics Subject Classification ID: 30C15
zbMATH DE Number: 5888157
zbMATH Keywords: partial sums of the Riemann zeta function
zbMATH Keywords: number of zeros
MaRDI profile type: Publication
Wikidata QID: Q58654526
full work available at URL: https://doi.org/10.1155/2011/909674
OpenAlex ID: W1532315023
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description: scientific article; zbMATH DE number 5888157