Rencontres de théorie analytique des nombres

Weyl sums with Multiplicative Coefficients and Joint Equidistribution

by Cynthia Bortolotto (ETH, Zurich, Suisse)

Salle Grisvard, IHP, 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.

Organized by

Régis de la Bretèche et Cathy Swaenepoel