Diophantine approximation of polynomials over ${\mathbb{F}}_q[t]$ satisfying a divisibility condition

Abstract

Let ${\mathbb{F}}_q[t]$ denote the ring of polynomials over ${\mathbb{F}}_q$, the finite field of $q$ elements. We prove an estimate for fractional parts of polynomials over ${\mathbb{F}}_q[t]$ satisfying a certain divisibility condition analogous to that of intersective polynomials in the case of integers. We then extend our result to consider linear combinations of such polynomials as well.

References in corpus (1)

• Equidistribution of polynomial sequences in function fields, with applications