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Nous décrivons dans cet article les algorithmes nécessaires à une implantation efficace de la méthode de Schoof pour le calcul du nombre de points sur une courbe elliptique dans un corps fini. Nous tentons d’unifier pour cela les idées d’Atkin et d’Elkies. En particulier, nous décrivons le calcul d’équations pour , premier, ainsi que le calcul efficace de facteurs des polynômes de division d’une courbe elliptique.
Introduction. The vanishing orders of L-functions at the centers of their functional equations are interesting objects to study as one sees, for example, from the Birch-Swinnerton-Dyer conjecture on the Hasse-Weil L-functions associated with elliptic curves over number fields.
In this paper we study the central zeros of the following types of L-functions:
(i) the derivatives of the Mellin transforms of Hecke eigenforms for SL₂(ℤ),
(ii) the Rankin-Selberg...
We define the notion overconvergent modular forms on where is a prime, and are positive integers and is prime to . We show that an overconvergent eigenform on of weight whose -eigenvalue has valuation strictly less than is classical.
Jacobi-like forms for a discrete subgroup Γ of SL(2,ℝ) are formal power series which generalize Jacobi forms, and they correspond to certain sequences of modular forms for Γ. Given a modular form f, a Jacobi-like form can be constructed by using constant multiples of derivatives of f as coefficients, which is known as the Cohen-Kuznetsov lifting of f. We extend Cohen-Kuznetsov liftings to quasimodular forms by determining an explicit formula for a Jacobi-like form associated to a quasimodular form....
We show that if is an extremal even unimodular lattice of rank with , then is generated by its vectors of norms and . Our result is an extension of Ozeki’s result for the case .
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