Weyl sums with Multiplicative Coefficients and Joint Equidistribution

par Cynthia Bortolotto (ETH, Zurich, Suisse)

lundi 18 mars 2024, 11:00 → 12:00 Europe/Paris

Salle Grisvard, IHP, Paris

In 1964, Hooley proved that for an irreducible polynomial $p$ in $\mathbb{Z}[x]$, the ratios $v/n$ for $v$ roots of the polynomial $p$ modulo $n$, are equidistributed modulo 1. We prove joint equidistribution of these roots of polynomial congruences and polynomial values. As part of the proof, we generalize a result of Montgomery and Vaughan regarding exponential sums with multiplicative coefficients to the setting of Weyl sums.