A refined Kurzweil type theorem in positive characteristic

作者：Kim Dong Han^*; Nakada Hitoshi; Natsui Rie

来源：Finite Fields and Their Applications, 2013, 20: 64-75.

DOI：10.1016/j.ffa.2012.12.002

• Formal Laurent series
• Inhomogeneous Diophantine approximation
• Kurzweil type theorem

We consider a Kurzweil type inhomogeneous Diophantine approximation theorem in the field of the formal Laurent series for a monotone sequence of approximation. We find a necessary and sufficient condition for irrational f and monotone increasing (l(n)) that there are infinitely many polynomials P and Q such that vertical bar Qf - P - g vertical bar %26lt; q(-n-ln), n = deg(Q) for almost every g. We also study some conditions for irrational f such that for all monotone increasing (l(n)) with Sigma q(-ln) = infinity there are infinitely many solutions for almost every g.

• 出版日期2013-3