Publication:
Almost all hyperharmonic numbers are not integers

dc.contributor.coauthorSertbaş, Doğa Can
dc.contributor.departmentGraduate School of Sciences and Engineering
dc.contributor.kuauthorGöral, Haydar
dc.contributor.schoolcollegeinstituteGRADUATE SCHOOL OF SCIENCES AND ENGINEERING
dc.date.accessioned2024-11-09T23:01:20Z
dc.date.issued2017
dc.description.abstractIt is an open question asked by Mezo that there is no hyperharmonic integer except 1. So far it has been proved that all hyperharmonic numbers are not integers up to order r = 25. In this paper, we extend the current results for large orders. Our method will be based on three different approaches, namely analytic, combinatorial and algebraic. From analytic point of view, by exploiting primes in short intervals we prove that almost all hyperharmonic numbers are not integers. Then using combinatorial techniques, we show that if n is even or a prime power, or r is odd then the corresponding hyperharmonic number is not integer. Finally as algebraic methods, we relate the integerness property of hyperharmonic numbers with solutions of some polynomials in finite fields. (C) 2016 Elsevier Inc. All rights reserved.
dc.description.indexedbyWOS
dc.description.indexedbyScopus
dc.description.openaccessYES
dc.description.publisherscopeInternational
dc.description.sponsoredbyTubitakEuN/A
dc.description.sponsorshipNesin Mathematics Village The authors are very grateful to the Nesin Mathematics Village for their support and warm hospitality during this work.
dc.description.volume171
dc.identifier.doi10.1016/j.jnt.2016.07.023
dc.identifier.eissn1096-1658
dc.identifier.issn0022-314X
dc.identifier.quartileQ3
dc.identifier.scopus2-s2.0-84991108843
dc.identifier.urihttps://doi.org/10.1016/j.jnt.2016.07.023
dc.identifier.urihttps://hdl.handle.net/20.500.14288/8218
dc.identifier.wos386418700026
dc.keywordsHyperharmonic numbers
dc.keywordsHarmonic numbers
dc.keywordsPrime number theory
dc.keywordsSpecial values
dc.keywordsZeta-function
dc.keywordsPrime
dc.language.isoeng
dc.publisherElsevier
dc.relation.ispartofJournal of Number Theory
dc.subjectMathematics
dc.titleAlmost all hyperharmonic numbers are not integers
dc.typeJournal Article
dspace.entity.typePublication
local.contributor.kuauthorGöral, Haydar
local.publication.orgunit1GRADUATE SCHOOL OF SCIENCES AND ENGINEERING
local.publication.orgunit2Graduate School of Sciences and Engineering
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