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

Tomohiro Ooto

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arXiv · 1512.04041

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

Tomohiro Ooto

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Abstract

In this paper, we study Diophantine exponents $w_n$ and $w_n ^{*}$ 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 $w_2-w_2 ^{*}$ 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.

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Tomohiro Ooto. 2015-12-13. Quadratic approximation in $\mathbb{F}_q ((T^{-1}))$. https://arxiv.org/abs/1512.04041

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