Peres--Schlag's nonempty-interior problem and a shifted-product variant for product sets

Guo-Dong Hong, Chong-Wei Liang, Chun-Yen Shen

We study finite-field analogues of the Peres--Schlag nonempty-interior problem for product sets. Given \(A\subseteq\mathbb F_p\), we ask when a suitable one-dimensional linear imag…