Fractional parts and their relations to the values of the Riemann zeta function

Handle URI:
http://hdl.handle.net/10754/625492
Title:
Fractional parts and their relations to the values of the Riemann zeta function
Authors:
Alabdulmohsin, Ibrahim ( 0000-0002-9387-5820 )
Abstract:
A well-known result, due to Dirichlet and later generalized by de la Vallée–Poussin, expresses a relationship between the sum of fractional parts and the Euler–Mascheroni constant. In this paper, we prove an asymptotic relationship between the summation of the products of fractional parts with powers of integers on the one hand, and the values of the Riemann zeta function, on the other hand. Dirichlet’s classical result falls as a particular case of this more general theorem.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Alabdulmohsin IM (2017) Fractional parts and their relations to the values of the Riemann zeta function. Arabian Journal of Mathematics. Available: http://dx.doi.org/10.1007/s40065-017-0184-2.
Publisher:
Springer Nature
Journal:
Arabian Journal of Mathematics
Issue Date:
6-Sep-2017
DOI:
10.1007/s40065-017-0184-2
Type:
Article
ISSN:
2193-5343; 2193-5351
Additional Links:
https://link.springer.com/article/10.1007%2Fs40065-017-0184-2
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorAlabdulmohsin, Ibrahimen
dc.date.accessioned2017-09-21T09:25:33Z-
dc.date.available2017-09-21T09:25:33Z-
dc.date.issued2017-09-06en
dc.identifier.citationAlabdulmohsin IM (2017) Fractional parts and their relations to the values of the Riemann zeta function. Arabian Journal of Mathematics. Available: http://dx.doi.org/10.1007/s40065-017-0184-2.en
dc.identifier.issn2193-5343en
dc.identifier.issn2193-5351en
dc.identifier.doi10.1007/s40065-017-0184-2en
dc.identifier.urihttp://hdl.handle.net/10754/625492-
dc.description.abstractA well-known result, due to Dirichlet and later generalized by de la Vallée–Poussin, expresses a relationship between the sum of fractional parts and the Euler–Mascheroni constant. In this paper, we prove an asymptotic relationship between the summation of the products of fractional parts with powers of integers on the one hand, and the values of the Riemann zeta function, on the other hand. Dirichlet’s classical result falls as a particular case of this more general theorem.en
dc.publisherSpringer Natureen
dc.relation.urlhttps://link.springer.com/article/10.1007%2Fs40065-017-0184-2en
dc.rightsThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.en
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/en
dc.titleFractional parts and their relations to the values of the Riemann zeta functionen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalArabian Journal of Mathematicsen
dc.eprint.versionPublisher's Version/PDFen
kaust.authorAlabdulmohsin, Ibrahimen
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