On the volume and the number of lattice of some semialgebraic sets

Ha Huy Vui, Tran Gia Loc

Let $f=(f_1,\dots ,f_m):{\mathbb{R}}^n⟶{\mathbb{R}}^m$ be a polynomial map; $G^f(r)=\{x\in {\mathbb{R}}^n:|f_i(x)|\le r,i=1,\dots ,m\}$. We show that if $f$ satisfies the Mikhailov…