SEQUENCES ASSOCIATED TO ELLIPTIC CURVES

GEZER B.

MATHEMATICAL REPORTS, vol.24, no.4, pp.821-847, 2022 (SCI-Expanded, Scopus)

  • Publication Type: Article / Article
  • Volume: 24 Issue: 4
  • Publication Date: 2022
  • Journal Name: MATHEMATICAL REPORTS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Page Numbers: pp.821-847
  • Keywords: elliptic curves, rational points on elliptic curves, division polynomials, elliptic divisibility sequences, squares, cubes, INTEGRAL POINTS, DIVISION POLYNOMIALS, EXPLICIT VALUATIONS, SQUARES, TORSION, TERMS, CUBES
  • Bursa Uludag University Affiliated: Yes

Abstract

Let E be an elliptic curve defined over a field K (with char(K) 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))