The local solubility for homogeneous polynomials with random coefficients over thin sets

Heejong Lee, Seungsu Lee, Kiseok Yeon

Let $d$ and $n$ be natural numbers greater or equal to $2$. Let $⟨\mathbf{a},{\nu }_{d,n}(\mathbf{x})⟩\in \mathbb{Z}[\mathbf{x}]$ be a homogeneous polynomial i…