Asymptotic behavior of the number of solutions for non-Archimedean Diophantine approximations with restricted denominators

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 especially consider approximations by rational functions whose denominators are powers of irreducible polynomials, and study the strong law of large numbers for the number of solutions of the inequalities under consideration. Key words: Laurent formal power series, metric Diophantine approximation, strong law of large numbers 2000 Mathematics Subject Classification. Primary 11J61; Secondary 11J83.

• Type: Journal
• Year: 2008
• Where: FFA
• Authors: Valérie Berthé, Hitoshi Nakada, Rie Natsui
• Keywords: Diophantine Approximation, FFA 2008, Formal Power Series, Laurent Formal Power