Weyl sums with Multiplicative Coefficients and Joint Equidistribution

Date/heure
21 mars 2024
14:30 - 15:30

Lieu
Salle Döblin

Oratrice ou orateur
Cynthia Bortolotto (ETH Zurich)

Catégorie d'évènement
Séminaire de Théorie des Nombres de Nancy-Metz


Résumé

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.