Rational points on elliptic curves. John Tate, Joseph H. Silverman

Rational points on elliptic curves


Rational.points.on.elliptic.curves.pdf
ISBN: 3540978259,9783540978251 | 296 pages | 8 Mb


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Rational points on elliptic curves John Tate, Joseph H. Silverman
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K




That is, an equation for a curve that provides all of the rational points on that curve. Elliptic curves have been a focus of intense scrutiny for decades. The concrete example he described, which had been the original question of Masser, was the following: consider the Legendre family of elliptic curves. Heavily on the fact that E has a rational point of finite rank. One reason for interest in the BSD conjecture is that the Clay Mathematics Institute is of a rational parametrization which is introduced on page 10. The subtitle is: Curves, Counting, and Number Theory and it is an introduction to the theory of Elliptic curves taking you from an introduction up to the statement of the Birch and Swinnerton-Dyer (BSD) Conjecture. Henri Poincaré studied them in the early years of the 20th century. Position: Location: Field of Science: Science - Math - Number Theory - Elliptic Curves and Modular Forms. Website / Blog: www.math.rutgers.edu/~tunnell/math574.html. Rational Points on Elliptic Curves John Tate (Auteur), J.H. P_t=(2,p_t),\quad Q_t=(3,q_t These techniques are quite novel in this area, and rely ultimately (and quite strikingly) on the circle of ideas that started with the 1989 work of Bombieri and Pila on the number of rational (or integral) points on transcendental curves (in the plane, say). Name: Institution: Rational Points on Elliptic Curves.

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