The work of Gross and Zagier on Heegner points and the derivatives of $L$-series

John Coates

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Displaying similar documents to “The work of Gross and Zagier on Heegner points and the derivatives of $L$ -series”

Arithmetic of elliptic curves and diophantine equations

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We give a survey of methods used to connect the study of ternary diophantine equations to modern techniques coming from the theory of modular forms.

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Gerhard Frey (1986)

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Elliptic curves and special values of L-series.

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Computing modular degrees using $L$ -functions

Christophe Delaunay (2003)

Journal de théorie des nombres de Bordeaux

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We give an algorithm to compute the modular degree of an elliptic curve defined over $ℚ$ . Our method is based on the computation of the special value at $s = 2$ of the symmetric square of the $L$ -function attached to the elliptic curve. This method is quite efficient and easy to implement.