Publication:
Sequences associated to elliptic curves

dc.contributor.authorGezer, Betül
dc.contributor.buuauthorGEZER, BETÜL
dc.contributor.departmentUludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü
dc.contributor.researcheridAAH-1547-2021
dc.date.accessioned2024-10-18T06:48:24Z
dc.date.available2024-10-18T06:48:24Z
dc.date.issued2022-01-01
dc.description.abstractLet E be an elliptic curve defined over a field K (with char(K)<is not equal to> 2) given by a Weierstrass equation and let P = (x, y) is an element of E(K) be a point. Then for each n >= 1 and some gamma is an element of K* we can write the x- and y-coordinates of the point [n]P as [n]P = (phi(n)(P)/psi(2)(n)(P), omega(n)(P)/psi(3)(n)(P)) = (gamma(2)G(n)(P)/F-n(2)(P), gamma H-3(n)(P)/F-n(3)(P))where phi(n), psi(n), omega n is an element of K[x, y], gcd(phi(n), psi(n)) = 1 andF-n(P) =gamma(1-n2)psi(n)(P), G(n)(P) = gamma(-2n2) phi(n)(P), H-n(P) = gamma(-3n2)omega(n)(P)are suitably normalized division polynomials of E. In this work we show the coefficients of the elliptic curve E can be defined in terms of the sequences of values (G(n)(P))(n >= 0) and (H-n(P))(n >= 0) of the suitably normalized division polynomials of E evaluated at a point P is an element of E(K). Then we give the general terms of the sequences (G(n)(P))(n >= 0) and (H-n(P))(n >= 0) associated to Tate normal form of an elliptic curve. As an application of this we determine square and cube terms in these sequences.
dc.identifier.endpage847
dc.identifier.issn1582-3067
dc.identifier.issue4
dc.identifier.startpage821
dc.identifier.urihttps://hdl.handle.net/11452/46712
dc.identifier.volume24
dc.identifier.wos000903636200016
dc.indexed.wosWOS.SCI
dc.language.isoen
dc.publisherEditura Acad Romane
dc.relation.bapKUAP(F)-2017/3
dc.relation.journalMathematical Reports
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.subjectIntegral points
dc.subjectDivision polynomials
dc.subjectExplicit valuations
dc.subjectSquares
dc.subjectTorsion
dc.subjectTerms
dc.subjectCubes
dc.subjectElliptic curves
dc.subjectRational points on elliptic curves
dc.subjectDivision polynomials
dc.subjectElliptic divisibility sequences
dc.subjectSquares
dc.subjectCubes
dc.subjectScience & technology
dc.subjectPhysical sciences
dc.subjectMathematics
dc.titleSequences associated to elliptic curves
dc.typeArticle
dspace.entity.typePublication
relation.isAuthorOfPublication6db39a60-7c04-4571-b528-8bee31473d4b
relation.isAuthorOfPublication.latestForDiscovery6db39a60-7c04-4571-b528-8bee31473d4b

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