The distribution of random polynomials with multiplicative coefficients

Date/heure
18 février 2021
14:30 - 15:30

Oratrice ou orateur
Brad Rodgers

Catégorie d'évènement
Analyse et théorie des nombres

A classic paper of Salem and Zygmund investigates the distribution of trigonometric polynomials whose coefficients are chosen randomly (say +1 or -1 with equal probability) and independently. Salem and Zygmund characterized the typical distribution of such polynomials (gaussian) and the typical magnitude of their sup-norms (a degree N polynomial typically has sup-norm of size $\sqrt{N\log N}$ for large N). In this talk we will explore what happens when a weak dependence is introduced between coefficients of the polynomials; namely we consider polynomials with coefficients given by random multiplicative functions. We consider analogues of Salem and Zygmund’s results, exploring similarities and some differences.

Special attention will be given to a beautiful point-counting argument introduced by Vaughan and Wooley which ends up being useful.

This is joint work with Jacques Benatar and Alon Nishry.