Diophantine approximation of polynomials over double-struck Fq[t] satisfying a divisibility condition

Abstract

Let double-struck Fq[t] denote the ring of polynomials over double-struck Fq, the finite field of q elements. We prove an estimate for fractional parts of polynomials over double-struck Fq[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.