Comments on the Links Between Modular Invariants, Simple Factors in the Jacobian of Fermat Curves, and Rational Triangular Billiards
Complex analytic geometry of complex parallelizable manifolds
Computing the cardinality of CM elliptic curves using torsion points
Let be an elliptic curve having complex multiplication by a given quadratic order of an imaginary quadratic field . The field of definition of is the ring class field of the order. If the prime splits completely in , then we can reduce modulo one the factors of and get a curve defined over . The trace of the Frobenius of is known up to sign and we need a fast way to find this sign, in the context of the Elliptic Curve Primality Proving algorithm (ECPP). For this purpose, we propose...
Congruences for Special Values of L-functions of Elliptic Curves with Complex Multiplication.
Corestriction of central simple algebras and families of Mumford-type
Let be a family of Mumford-type, that is, a family of polarized complex abelian fourfolds as introduced by Mumford in [9]. This family is defined starting from a quaternion algebra over a real cubic number field and imposing a condition to the corestriction of such . In this paper, under some extra conditions on the algebra , we make this condition explicit and in this way we are able to describe the polarization and the complex structures of the fibers. Then, we look at the non simple -fibers...
Courbes elliptiques et formes modulaires de poids 3/2
Courbes elliptiques, fonctions L , et tours cyclotomiques.
Cycles de Hodge absolus et périodes des intégrales des variétés abéliennes. (Rédigé par J. L. Brylinski)