ENGE, Andreas; SCHERTZ, Reinhard

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Licence d’utilisation du document

ENGE, Andreas
Laboratoire d'informatique de l'École polytechnique [Palaiseau] [LIX]
Algorithmic number theory for cryptology [TANC]

SCHERTZ, Reinhard
Institut für Mathematik [Augsburg]

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Article de revue

Ce document a été publié dans

Acta Arithmetica. 2005, vol. 118, n° 2, p. 129-141

Instytut Matematyczny PAN

Résumé en anglais

We examine a class of functions on $X_0 (N)$ where $N$ is the product of two arbitrary primes. The functions are built as products of Dedekind's $\eta$-function and play a role in the construction of elliptic curves with complex multiplication. We show how to determine the modular polynomials relating them to the absolute modular invariant $j$ and prove different properties of these polynomials. In particular, we show that they provide models for the modular curves $X_0 (N)$.< Réduire

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Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251