Vlad Matei
Simion Stoilow Institute of Mathematics of the Romanian Academy, Bucharest, Romania

In joint work in progress with Lior Bary Soroker and Daniele Garzoni we look at polynomials $f(t_1, t_2,\ldots, t_n, X)\in \mathbb{Q}[t_1,\ldots, t_n, X]$ which satisfy the condition that $f(t_1^{l_1},\ldots, t_n^{l_n}, X)$ is absolutely irreducible for any tuple $(l_1,\ldots, l_n)$ of positive. and $\deg_X(f)\geq 2$. We show that that density of specializations $f(a_1^{m_1},\ldots, a_n^{m_n}, X)$ where $a_1,\ldots, a_n$ are fixed multiplicatively independent elements and $1\leq m_i\leq N$ is $1$ as $N$ goes to infinity.