1. Fonctions multiplicatives, sommes d'exponentielles, et loi des grands nombres
- Author
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Gérald Tenenbaum, Institut Élie Cartan de Lorraine (IECL), and Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)
- Subjects
strong law of large numbers ,General Mathematics ,multiplicative coefficients ,01 natural sciences ,Upper and lower bounds ,arithmetical progressions ,Law of large numbers ,0103 physical sciences ,0101 mathematics ,exponential sums ,short sums of multipli-cative functions ,Mathematics ,multiplicative weights ,Discrete mathematics ,Unit function ,010102 general mathematics ,Multiplicative function ,Multiplicative order ,16. Peace & justice ,[MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT] ,Exponential function ,AMS 11N37, (11L07, 11N64, 60F15) ,Multiplicative inverse ,010307 mathematical physics ,Mean values of non-negative multiplicative functions ,Order of magnitude - Abstract
International audience; We provide essentially optimal, effective conditions to ensure that, when available, the Halberstam–Richert upper bound for the mean value of a non-negative multiplicative function actually furnishes the true order of magnitude. This is applied, in particular, to short sums of multiplicative functions over arithmetic progressions, to exponential sums with multiplicative coefficients, and to strong law of large numbers with multiplicative weights.; Nous donnons des conditions suffisantes effectives quasi-optimales pour que la majoration de Halberstam–Richert fournisse effectivement l'ordre de grandeur de la valeur moyenne d'une fonction multiplicative positive ou nulle.
- Published
- 2016