Publication:
On Cardinality Of Character Sums With Beatty Sequences Associated With Composite Modules

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dc.contributor.authorAllakov Ismail
dc.contributor.authorFatanah binti Deraman
dc.contributor.authorSiti Hasana binti Sapar
dc.contributor.authorShahrina binti Ismail
dc.date.accessioned2024-06-16T06:29:08Z
dc.date.available2024-06-16T06:29:08Z
dc.date.issued2023
dc.date.submitted2024-2-28
dc.description.abstractNon homogeneous Beatty sequences play important rules in Wythoff games and invariant games such as on how to beat your Wytoff games opponent on three fronts and give properties into a decision of the procedure relying only on a few algebraic tests. This paper discusses on the cardinality of character sums and their estimation with respect to non homogeneous Beatty sequences βα = ⌊αn + β : n = 1, 2, 3...⌋ where β in real numbers and α greater than zero is irrational. In order to estimate the cardinality, the discrepancy is used to measure the number of uniform distribution for Beatty sequences. Pigeonhole principle is discussed on the estimation of the fractional part of Beatty sequences involve. Meanwhile, Cauchy inequalities is applied to expand the double character sums. Then, the cardinality of double character sums is obtained by applying the extension properties of additive and multiplicative character sums. The result obtained is depend on the existing of identity of additive and multiplicative character sums and the uniformly distribution modulo 1. The result of the estimation in this study over composite modules is more general compared to previous studies, which only cover prime modules.
dc.identifier.doi10.22405/2226-8383-2023-24-5-5-15
dc.identifier.epage15
dc.identifier.issn2226-8383
dc.identifier.issue5
dc.identifier.spage6
dc.identifier.urihttps://www.chebsbornik.ru/jour/article/view/1617/1135
dc.identifier.urihttps://oarep.usim.edu.my/handle/123456789/19489
dc.identifier.urihttps://www.scopus.com/record/display.uri?eid=2-s2.0-85186204647&origin=resultslist&sort=plf-f&src=s&sid=f42f304a353d4f470e63a34063d29015&sot=b&sdt=b&s=TITLE-ABS-KEY%28On+Cardinality+Of+Character+Sums+With+Beatty+Sequences+Associated+With+Composite+Modules%29&sl=103&sessionSearchId=f42f304a353d4f470e63a34063d29015&relpos=0
dc.identifier.volume24
dc.language.isoen_US
dc.publisherTula State Lev Tolstoy Pedagogical University
dc.relation.ispartofCHEBYSHEVSKII SBORNIK
dc.relation.issn2587-7119
dc.relation.journalChebyshevskii Sbornik
dc.subjectadditive characters
dc.subjectBeatty sequences
dc.subjectcardinality
dc.subjectestimation
dc.subjectfinite groups
dc.subjectirrational numbers
dc.subjectmultiplicative character
dc.subjectnumber theory
dc.subjectpigeonhole principle
dc.subjectrational number
dc.subjectsum of characters
dc.titleOn Cardinality Of Character Sums With Beatty Sequences Associated With Composite Modules
dc.title.alternativeОб оценке сумм характеров с последовательностями Битти, связанными с составными модулями
dc.typetext::journal::journal article::research article
dspace.entity.typePublication
oaire.citation.endPage15
oaire.citation.issue5
oaire.citation.startPage5
oaire.citation.volume24
oairecerif.author.affiliation#PLACEHOLDER_PARENT_METADATA_VALUE#
oairecerif.author.affiliation#PLACEHOLDER_PARENT_METADATA_VALUE#
oairecerif.author.affiliation#PLACEHOLDER_PARENT_METADATA_VALUE#
oairecerif.author.affiliationUniversiti Sains Islam Malaysia

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