论文信息 - Generalization of Manin's conditional algorithm

Generalization of Manin's conditional algorithm

In a lecture [16] delivered at the conference on “Utilisation des calculateurs en mathématiques pures” in France, we developed some ideas regarding the implementation of Manin's conditional algorithm [7] for computing the rank and a basis of the group of rational points on an elliptic curve C over the rationals Ø. The aim of the present paper is to discuss to which extent this algorithm can be generalized to elliptic curves C defined over an arbitrary finite-algebraic number field K. Furthermore, certain problems concerning the implementation of the generalized algorithm will be treated. Some results obtained in this connection seem to be also per se of interest. In an appendix we shall give complete proofs of the assertions made in sections 1,4, and 6.

Horst Günter Zimmer | H. Zimmer

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