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arXiv.org e-Print Archive
Preprint . 2016
Data sources: arXiv.org e-Print Archive
https://dx.doi.org/10.48550/ar...
Article . 2016
License: arXiv Non-Exclusive Distribution
Data sources: Datacite
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Riemann's Zeta Function: The alternating Xi-Function Xia(s)

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2016Embargo end date: 01 Jan 2016Publisher:arXiv
Authors: Van Malderen, Renaat;

doi: 10.48550/arxiv.1610.04344

arXiv: http://arxiv.org/abs/1610.04344

Riemann's Zeta Function: The alternating Xi-Function Xia(s)

Abstract

As well known, the study of Riemanns zeta function ��(s) involves the related entire function ��(s). A close relative of ��(s) is the alternating zeta function ��(s). Similar to ��(s), also ��(s) has a corresponding entire function ��_a (s). After establishing its definition and a related functional equation, formulas based on incomplete gamma functions are worked out, allowing to numerically evaluate ��_a (s). Examples verifying the obtained formulas are included.

Keywords

Mathematics - Number Theory, FOS: Mathematics, Number Theory (math.NT)

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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