Effective solution of two simultaneous Pell equations by the elliptic logarithm method
Efficient computation of addition chains
The aim of this paper is to present a unifying approach to the computation of short addition chains. Our method is based upon continued fraction expansions. Most of the popular methods for the generation of addition chains, such as the binary method, the factor method, etc..., fit in our framework. However, we present new and better algorithms. We give a general upper bound for the complexity of continued fraction methods, as a function of a chosen strategy, thus the total number of operations required...
Ein Beitrag zur analytischen Zahlentheorie.
Einheitenberechnung in kubischen Körpern mittels des Jacobi-Perronschen Algorithmus aus der Rechenanlage.
Elementary proof of Yu. V. Nesterenko expansion of the number zeta(3) in continued fraction.
Elliptic Carmichael numbers and elliptic Korselt criteria
Elliptic curves with j-invariant equals 0 or 1728 over a finite prime field.
Let p be a prime number, p ≠ 2,3 and Fp the finite field with p elements. An elliptic curve E over Fp is a projective nonsingular curve of genus 1 defined over Fp. Each one of these curves has an isomorphic model given by an (Weierstrass) equation E: y2 = x3 + Ax + B, A,B ∈ Fp with D = 4A3 + 27B2 ≠ 0. The j-invariant of E is defined by j(E) = 1728·4A3/D.The aim of this note is to establish some results concerning the cardinality of the group of points on elliptic curves over Fp with j-invariants...
Enumerating quartic dihedral extensions of with signatures
In a previous paper, we have given asymptotic formulas for the number of isomorphism classes of -extensions with discriminant up to a given bound, both when the signature of the extensions is or is not specified. We have also given very efficient exact formulas for this number when the signature is not specified. The aim of this paper is to give such exact formulas when the signature is specified. The problem is complicated by the fact that the ray class characters which appear are not all genus characters....
Equivalences between elliptic curves and real quadratic congruence function fields
In 1994, the well-known Diffie-Hellman key exchange protocol was for the first time implemented in a non-group based setting. Here, the underlying key space was the set of reduced principal ideals of a real quadratic number field. This set does not possess a group structure, but instead exhibits a so-called infrastructure. More recently, the scheme was extended to real quadratic congruence function fields, whose set of reduced principal ideals has a similar infrastructure. As always, the security...
Erratum
Erratum “On the computation of quadratic -class groups”
Etude algorithmique de réseaux construits avec la forme trace. (Algorithmic study of lattices constructed by means of the trace form).
Étude du problème du logarithme discret dans
Euler constants for arithmetic progressions
Evaluation effective du nombre d'entiers n tels que φ(n) ≤ x
Evaluation of triple Euler sums.
Evaluations of -fold Euler/Zagier sums: a compendium of results for arbitrary .
Exceptional units and numbers of small Mahler measure.
Experimental determination of Apéry-like identities for .
Experimental evaluation of Euler sums.