Polynomial values and generators with missing digits in finite fields
Cécile Dartyge, Christian Mauduit, Andràs Sárközy · Functiones et Approximatio Commentarii Mathematici · 2015
We consider the linear vector space formed by the elements of the finite field $\mathbb{F}_q$ with $q=p^r$ over $\mathbb{F}_p$. Then the elements $x$ of $\mathbb{F}_q$ have a unique representation in the form $x=\sum_{j=1}^r c_ja_j$ with $c_j\in\mathbb{F}_p$; the coefficients $c_j$ will be called digits. Let $\mathbb{D}$ be a subset of $\mathbb{F}_p$ with $2\le |\mathbb{D}|