Publication: Sequences associated to elliptic curves
dc.contributor.author | Gezer, Betül | |
dc.contributor.buuauthor | GEZER, BETÜL | |
dc.contributor.department | Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü | |
dc.contributor.researcherid | AAH-1547-2021 | |
dc.date.accessioned | 2024-10-18T06:48:24Z | |
dc.date.available | 2024-10-18T06:48:24Z | |
dc.date.issued | 2022-01-01 | |
dc.description.abstract | Let 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.endpage | 847 | |
dc.identifier.issn | 1582-3067 | |
dc.identifier.issue | 4 | |
dc.identifier.startpage | 821 | |
dc.identifier.uri | https://hdl.handle.net/11452/46712 | |
dc.identifier.volume | 24 | |
dc.identifier.wos | 000903636200016 | |
dc.indexed.wos | WOS.SCI | |
dc.language.iso | en | |
dc.publisher | Editura Acad Romane | |
dc.relation.bap | KUAP(F)-2017/3 | |
dc.relation.journal | Mathematical Reports | |
dc.relation.publicationcategory | Makale - Uluslararası Hakemli Dergi | |
dc.rights | info:eu-repo/semantics/closedAccess | |
dc.subject | Integral points | |
dc.subject | Division polynomials | |
dc.subject | Explicit valuations | |
dc.subject | Squares | |
dc.subject | Torsion | |
dc.subject | Terms | |
dc.subject | Cubes | |
dc.subject | Elliptic curves | |
dc.subject | Rational points on elliptic curves | |
dc.subject | Division polynomials | |
dc.subject | Elliptic divisibility sequences | |
dc.subject | Squares | |
dc.subject | Cubes | |
dc.subject | Science & technology | |
dc.subject | Physical sciences | |
dc.subject | Mathematics | |
dc.title | Sequences associated to elliptic curves | |
dc.type | Article | |
dspace.entity.type | Publication | |
relation.isAuthorOfPublication | 6db39a60-7c04-4571-b528-8bee31473d4b | |
relation.isAuthorOfPublication.latestForDiscovery | 6db39a60-7c04-4571-b528-8bee31473d4b |