Asymptotic Behavior of the Number of Solutions for Non-Archimedean Diophantine Approximations with Restricted Denominators
Abstract
We consider metric results for the asymptotic behavior of the number of solutions of Diophantine approximation inequalities with restricted denominators for Laurent formal power series with coefficients in a finite field. We consider, in particular, approximations by rational functions whose denominators are powers of irreducible polynomials, and we study the strong law of large numbers for solutions of the inequalities under consideration