“Counting rational points on thin sets of type II”
Martedì 31 Marzo 2026, ore 14:30 - Aula 2AB40 - Dante Bonolis (TU Graz)
Abstract
For $n>0$ consider an absolutely irreducible polynomial $F(Y,X_1,…,X_n)$, monic in $Y$. Let $N(F,B)$ be the number of integral points $\mathbf{x}$ of height at most $B$ such that the polynomial $F(Y,\mathbf{x})$ is solvable over the integers. Under suitable assumptions, we are going to show that $N(F,B) \ll log(|F|)^{c} B^{(n-1 + 1/(n+1) + \epsilon)}$.
This talk is based on joint works with Emmanuel Kowalski, Lillian Pierce and Katherine Woo.
