Comportement local des fonctions continues sur un compact régulier d'un corps local
We describe the average behaviour of the Brjuno function Φ in the neighbourhood of any given point of the unit interval. In particular, we show that the Lebesgue set of Φ is the set of Brjuno numbers and we find the asymptotic behaviour of the modulus of continuity of the integral of Φ.
In this note, we show that the counting function of the number of composite positive integers such that is a prime is of order of magnitude at least and at most .
We consider a rational function which is ‘lacunary’ in the sense that it can be expressed as the ratio of two polynomials (not necessarily coprime) having each at most a given number of terms. Then we look at the possible decompositions , where are rational functions of degree larger than 1. We prove that, apart from certain exceptional cases which we completely describe, the degree of is bounded only in terms of (and we provide explicit bounds). This supports and quantifies the intuitive...
Nous établissons une version de la conjecture de Manin pour le plan projectif éclaté en trois points alignés, le corps de base étant un corps global de caractéristique positive.
Le but de cet article est d’expliquer comment calculer exactement le nombre de classes d’isomorphismes d’extensions abéliennes de en degré inférieur ou égal à et de discriminant majoré par une borne donnée. On parvient par exemple à calculer le nombre de corps cubiques cycliques de discriminant inférieur ou égal à .