The splitting of primes in division fields of elliptic curves.
The uniform primality conjecture for elliptic curves
The Way to the Proof of Fermat’s Last Theorem
The work of Gross and Zagier on Heegner points and the derivatives of -series
Théorie d'Iwasawa p-adique locale et globale.
Thetanullwerte: from periods to good equations.
We will show the utility of the classical Jacobi Thetanullwerte for the description of certain period lattices of elliptic curves, providing equations with good arithmetical properties. These equations will be the starting point for the construction of families of elliptic curves with everywhere good reduction.[Proceedings of the Primeras Jornadas de Teoría de Números (Vilanova i la Geltrú (Barcelona), 30 June - 2 July 2005)].
Torsion and Tamagawa numbers
Let be a number field, and let be an abelian variety. Let denote the product of the Tamagawa numbers of , and let denote the finite torsion subgroup of . The quotient is a factor appearing in the leading term of the -function of in the conjecture of Birch and Swinnerton-Dyer. We investigate in this article possible cancellations in this ratio. Precise results are obtained for elliptic curves over or quadratic extensions , and for abelian surfaces . The smallest possible ratio...
Torsion des courbes elliptiques sur les corps cubiques
On donne la liste (à un élément près) des nombres premiers qui sont l’ordre d’un point de torsion d’une courbe elliptique sur un corps de nombres de degré trois.
Torsion groups of elliptic curves over quadratic fields
Torsion points on elliptic curves and galois module structure.
Torsion points on elliptic curves and q-coeffincients of modular forms.
Torsion subgroups of elliptic curves with non-cyclic torsion over ℚ in elementary abelian 2-extensions of ℚ
Travaux de Kolyvagin et Rubin
Travaux de Wiles (et Taylor, ...), partie I
Travaux de Wiles (et Taylor, ...), partie II
Triples of Positive Integers with the same Sum and the same Product
It is proved that for every k there exist k triples of positive integers with the same sum and the same product.
Trivial Selmer groups and even partitions of a graph.
Twisted exponential sums over points of elliptic curves
Twists of Hessian Elliptic Curves and Cubic Fields
In this paper we investigate Hesse’s elliptic curves , and construct their twists, over quadratic fields, and over the Galois closures of cubic fields. We also show that is a twist of over the related cubic field when the quadratic field is contained in the Galois closure of the cubic field. We utilize a cubic polynomial, , to parametrize all of quadratic fields and cubic ones. It should be noted that is a twist of as algebraic curves because it may not always have any rational points...
Über die Fermat-Vermutung.