| Gross-zagier Theorem |
Website Links For Point |
Information AboutGross-zagier Theorem |
| CATEGORIES ABOUT HEEGNER POINT | |
| algebraic number theory | |
| elliptic curves | |
|
The Gross-Zagier theorem describes the height of Heegner points in terms of a derivative of the L-function of the elliptic curve at the point ''s''=1. In particular if the elliptic curve has (analytic) rank 1, then the Heegner points can be used to construct a rational point on the curve of infinite order (so the Mordell-Weil Group has rank at least 1). More generally, together with Kohnen, Gross and Zagier showed that Heegner points could be used to construct rational points on the curve for each positive integer ''n'', and the heights of these points were the coefficients of a modular form of weight 3/2. Kolyvagin later used Heegner points to construct Euler System s, and used this to prove much of the Birch-Swinnerton-Dyer Conjecture for rank 1 elliptic curves. Shouwu Zhang generalized Gross-Zagier theorem from elliptic curve to the case of Abelian Variety . REFERENCES
|
|
|