Quadratic approximation in ${\mathbb{F}}_q((T^{-1}))$

Abstract

In this paper, we study Diophantine exponents $w_n$ and $w_n^{\ast }$ for Laurent series over a finite field. Especially, we deal with the case $n=2$, that is, quadratic approximation. We first show that the range of the function $w_2-w_2^{\ast }$ is exactly the closed interval $[0,1]$. Next, we estimate an upper bound of the exponent $w_2$ of continued fractions with low complexity partial quotients.

23 pages

References in corpus (1)

• Mahler's classification and a certain class of $p$-adic numbers