منابع مشابه
Elliptic Nets and Elliptic Curves
Elliptic divisibility sequences are integer recurrence sequences, each of which is associated to an elliptic curve over the rationals together with a rational point on that curve. In this paper we present a higher-dimensional analogue over arbitrary base fields. Suppose E is an elliptic curve over a field K, and P1, . . . , Pn are points on E defined over K. To this information we associate an ...
متن کاملElliptic Nets and Points on Elliptic Curves
(2) hn divides hm whenever n divides m. They have attracted number theoretical and combinatorial interest as some of the simplest nonlinear recurrence sequences (see [3] for references), but for us their interest lives in the underlying geometry: Ward demonstrates that an elliptic divisibility sequence arises from any choice of elliptic curve over Q and rational point on that curve. Theorem 1 (...
متن کاملElliptic Cohomology and Elliptic Curves (felix Klein
Lecture notes for a series of talks given in Bonn, June 2015. Most of the topics covered touched in one way or another on the role of power operations in elliptic cohomology. In June of 2015 I gave a series of six lectures (the Felix Klein lectures) in Bonn. These are some of my lecture notes for those talks. I had hoped to polish them more carefully, but that hasn’t happend yet, and at this po...
متن کاملGeneralized Jacobian and Discrete Logarithm Problem on Elliptic Curves
Let E be an elliptic curve over the finite field F_{q}, P a point in E(F_{q}) of order n, and Q a point in the group generated by P. The discrete logarithm problem on E is to find the number k such that Q = kP. In this paper we reduce the discrete logarithm problem on E[n] to the discrete logarithm on the group F*_{q} , the multiplicative group of nonzero elements of Fq, in the case where n | q...
متن کاملElliptic Curves
This is a introduction to some aspects of the arithmetic of elliptic curves, intended for readers with little or no background in number theory and algebraic geometry. In keeping with the rest of this volume, the presentation has an algorithmic slant. We also touch lightly on curves of higher genus. Readers desiring a more systematic development should consult one of the references for further ...
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ژورنال
عنوان ژورنال: Algebra & Number Theory
سال: 2011
ISSN: 1944-7833,1937-0652
DOI: 10.2140/ant.2011.5.197