Concentration simultan\'ee de fonctions additives

TL;DR

This paper investigates how multiple additive functions simultaneously concentrate along polynomial shifts, extending a classical result by Halász from 1975 under certain conditions.

Contribution

It introduces a new extension of Halász's 1975 result to the case of multiple additive functions along polynomial shifts with a mild restriction.

Findings

Extended Halász's result to multiple additive functions

Demonstrated concentration phenomena along polynomial shifts

Provided conditions under which the extension holds

Abstract

We study the simultaneous concentration of the values of several additive functions along polynomial shifts. Under a slight restriction, this yields an extension of a result from Hal\'asz in 1975.