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Article: Universal sums of generalized heptagonal numbers

TitleUniversal sums of generalized heptagonal numbers
Authors
Kamaraj, RamanujamKane, BenOishi-Tomiyasu, Ryoko
KeywordsDiophantine equations
Quadratic forms
Sums of polygonal numbers
Theta functions
Issue Date1-Aug-2023
PublisherElsevier
Citation
Journal of Number Theory, 2023, v. 249, p. 500-536 How to Cite?
DOI: http://dx.doi.org/10.1016/j.jnt.2023.02.003
Abstract

In this paper, we consider representations of integers as sums of heptagonal numbers with a prescribed number of repeats of each heptagonal number appearing in the sum. In particular, we investigate the classification of such sums which are universal, i.e., those that represent every positive integer. We prove an explicit finite bound such that a given sum is universal if and only if it represents positive integer up to the given bound.



Persistent Identifierhttp://hdl.handle.net/10722/340885
ISSN
0022-314X
2022 Impact Factor: 0.7
2020 SCImago Journal Rankings: 0.634
ISI Accession Number ID
WOS:000982504700001

 

DC FieldValueLanguage
dc.contributor.authorKamaraj, Ramanujam-
dc.contributor.authorKane, Ben-
dc.contributor.authorOishi-Tomiyasu, Ryoko-
dc.date.accessioned2024-03-11T10:48:01Z-
dc.date.available2024-03-11T10:48:01Z-
dc.date.issued2023-08-01-
dc.identifier.citationJournal of Number Theory, 2023, v. 249, p. 500-536-
dc.identifier.issn0022-314X-
dc.identifier.urihttp://hdl.handle.net/10722/340885-
dc.description.abstract<p>In this paper, we consider representations of integers as sums of heptagonal numbers with a prescribed number of repeats of each heptagonal number appearing in the sum. In particular, we investigate the classification of such sums which are universal, i.e., those that represent every positive integer. We prove an explicit finite bound such that a given sum is universal if and only if it represents positive integer up to the given bound.</p><p><br></p>-
dc.languageeng-
dc.publisherElsevier-
dc.relation.ispartofJournal of Number Theory-
dc.subjectDiophantine equations-
dc.subjectQuadratic forms-
dc.subjectSums of polygonal numbers-
dc.subjectTheta functions-
dc.titleUniversal sums of generalized heptagonal numbers-
dc.typeArticle-
dc.identifier.doi10.1016/j.jnt.2023.02.003-
dc.identifier.scopuseid_2-s2.0-85151902000-
dc.identifier.volume249-
dc.identifier.spage500-
dc.identifier.epage536-
dc.identifier.eissn1096-1658-
dc.identifier.isiWOS:000982504700001-
dc.identifier.issnl0022-314X-

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