Rencontres de théorie analytique des nombres

Sign changes of partial sums of random multiplicative functions

by Marco Aymone (Universidade Federal de Minas Gerais (UFMG), Brésil et Aix-Marseille Université)

Salle 201, IHP, Paris

Salle 201, IHP, Paris


Resolving a question of Lévy, Wintner started the study of a Rademacher random multiplicative function in the 40's. This is a genuine multiplicative function supported on the squarefree integers such that its values at primes are given by ± 1 independent random variables. Several results concerning upper and omega bounds, low and high moments and central limit theorems have been proved. In this talk I will discuss sign changes of the partial sums of two models of random multiplicative functions: the Rademacher case and the completely multiplicative random case. I will also discuss the results in the literature about sign changes of the partial sums of the deterministic counterparts such as the Liouville and the Möbius function.

Organized by

Régis de la Bretèche