Computing the summation of the Möbius function.
Construction of binomial sums for and polylogarithmic constants inspired by BBP formulas.
Convergence acceleration of alternating series.
Corps sextiques contenant un corps cubique (III)
Corps sextiques contenant un corps quadratique (I)
Corps sextiques contenant un corps quadratique (II)
Corps sextiques primitifs
Nous décrivons quatre tables de corps sextiques primitifs (une par signature). Les tables fournissent pour chaque corps, le discriminant, le groupe de Galois de la clôture galoisienne et un polynôme définissant le corps.
Corps sextiques primitifs (IV)
Counting points in medium characteristic using Kedlaya's algorithm.
Counting points on elliptic curves over finite fields
We describe three algorithms to count the number of points on an elliptic curve over a finite field. The first one is very practical when the finite field is not too large ; it is based on Shanks's baby-step-giant-step strategy. The second algorithm is very efficient when the endomorphism ring of the curve is known. It exploits the natural lattice structure of this ring. The third algorithm is based on calculations with the torsion points of the elliptic curve [18]. This deterministic polynomial...
Cribrum algebraicum oder die cofunctionale Entstehung der Primzahlen.
De l’euclidianité de et pour la norme
Cet article a pour objectif de présenter un algorithme permettant de montrer, à l’aide d’un ordinateur, l’euclidianité pour la norme du sous-corps réel maximal du corps cyclotomique où , corps totalement réel de degré et de discriminant , et plus précisément de prouver que . La méthode utilisée permet par ailleurs de prouver que pour , on a également (conjecture de H. Cohn et J. Deutsch). Les résultats relatifs à ce cas sont exposés en fin d’article.
Decomposing rational numbers
Dedekind cotangent sums
Denominators of Igusa class polynomials
In [22], the authors proved an explicit formula for the arithmetic intersection number on the Siegel moduli space of abelian surfaces, under some assumptions on the quartic CM field . These intersection numbers allow one to compute the denominators of Igusa class polynomials, which has important applications to the construction of genus curves for use in cryptography. One of the main tools in the proof was a previous result of the authors [21] generalizing the singular moduli formula of Gross...
Derived sequences.
Détermination de courbes elliptiques pour la conjecture de Szpiro
Determining Mills' constant and a note on Honaker's problem.
Digits and continuants in euclidean algorithms. Ergodic versus tauberian theorems
We obtain new results regarding the precise average-case analysis of the main quantities that intervene in algorithms of a broad Euclidean type. We develop a general framework for the analysis of such algorithms, where the average-case complexity of an algorithm is related to the analytic behaviour in the complex plane of the set of elementary transformations determined by the algorithms. The methods rely on properties of transfer operators suitably adapted from dynamical systems theory and provide...
Diophantine equations of matching games II