From the Taniyama-Shimura conjecture to Fermat's last theorem
Galois Properties of Torsion Points on Abelian Varieties.
Galois theory, elliptic curves, and root numbers
Gap orders of meromorphic functions on Riemann surfaces.
Gauss Sums and Elliptic Functions. I. The Kummer Sum.
General Selmer groups and critical values of Hecke L-functions.
Généralités sur les courbes elliptiques
Generalizing the Birch-Stephens theorem. I. Modular curves.
Global units and ideal class groups.
Good reduction of elliptic curves in abelian extensions.
Heegner Points on X ... (11)
Hilbert functions and Witt functions. An identity for congruences of Atkin and of Swinnerton-Dyer type.
Hyperelliptic Curves with zero Hasse-Witt-Matrix.
Ideal arithmetic and infrastructure in purely cubic function fields
This paper investigates the arithmetic of fractional ideals of a purely cubic function field and the infrastructure of the principal ideal class when the field has unit rank one. First, we describe how irreducible polynomials decompose into prime ideals in the maximal order of the field. We go on to compute so-called canonical bases of ideals; such bases are very suitable for computation. We state algorithms for ideal multiplication and, in the case of unit rank one and characteristic at least five,...
Indépendance algébrique de nombres transcendants: quelques résultats récents.
Indices of double coverings of genus 1 over -adic fields
Infinite rank of elliptic curves over
If E is an elliptic curve defined over a quadratic field K, and the j-invariant of E is not 0 or 1728, then has infinite rank. If E is an elliptic curve in Legendre form, y² = x(x-1)(x-λ), where ℚ(λ) is a cubic field, then has infinite rank. If λ ∈ K has a minimal polynomial P(x) of degree 4 and v² = P(u) is an elliptic curve of positive rank over ℚ, we prove that y² = x(x-1)(x-λ) has infinite rank over .
Integer points on curves of genus 1
Integral points on abelian surfaces are widely spaced
Integral points on elliptic curves defined by simplest cubic fields.