Niveau: Supérieur, Doctorat, Bac+8
Proc. London Math. Soc. (3) 96 (2008) 107–135. Moyennes de certaines fonctions multiplicatives sur les entiers friables, 2 Guillaume Hanrot, Gerald Tenenbaum & Jie Wu Abstract. We derive new, very precise estimates for averages of arithmetic functions over friable integers from analytic information on their associated Dirichlet series. These yield significant improvements upon available results in classical cases, in particular concerning the e?ective expansion of “abstract” main terms of de Bruijn type. These results also permit new applications, linked to the solubility of polynomial equations. AMS Subject classification. 11N37, 11N25, 11M41, 11C08. Keywords. Friable integers, averages of multiplicative functions, polynomials, Dedekind zeta functions, solubility of polynomial equations. Sommaire 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Objectif . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
- serie de dirichlet
- multiplicative functions
- friable integers
- entiers friables
- functions over friable
- fonctions zetas de dedekind generalisees
- functions