Courbes modulaires et 11-rang de corps quadratiques

Courbes modulaires et 11-rang de corps quadratiques

TABLE DES MATI`ERES Introduction 1. Structure galoisienne de courbes modulaires 2. Le cas p = 23 3. Méthode et Résultats Remerciements Bibliographie Nous construisons 53 corps quadratiques imaginaires ayant un 11-rangégaì a 3, et sept corps quadratiques réels de 11-rangégaì a 2. Ce sont, ` a notre connaissance, les premiers exemples de tels corps. We construct 53 imaginary quadratic fields of 1...

Courbes hyperelliptiques à multiplications réelles et une construction de Shih

Let r and p be distinct prime numbers, let K = Q(cos 2π r ), and let F be the residue field of K at a place above p. When the image of (2 − 2 cos 2π r ) in F is not a square, we describe a geometric construction of a regular extension of K(t) with Galois group PSL2(F). This extension corresponds to a covering of P/K of “signature (r, p, p)” in the sense of [3, sec. 6.3], and its existence is pr...

Simulation dynamique de corps biologiques et changements de topologie interactifs

Formes Modulaires Et Représentations -adiques

(2π)Γ(s)Lτ (s) is invariant under s 7→ 12 − s. The Ramanujan conjecture affirms that the roots of the polynomial Hp are of absolute value p −11/2 (i.e. that |τ(p)| < 2p). These properties, proven or conjectural, are similar to conjectural properties of zeta functions of algebraic varieties over Q. Suggested by this, in a first approximation, it is tempting to interpret the function Lτ as the ze...

Assimilation de données images : application au suivi de courbes et de champs de vecteurs

This thesis presents the use of sequential and variational methods for tracking applications in image se-quences. These techniques aim at estimating a system state from a dynamical model and a set of noisy andsparse observations. Sequential methods are usually used in computer vision community but limited to smalldimensional state spaces. In metorology or oceanography, data assimila...