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

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.

Quadratic approximation in $F_{q} ((T^{- 1}))$

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Quadratic approximation in $F_{q} ((T^{- 1}))$

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Quadratic approximation in Fq((T−1))Fq​((T−1))

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Quadratic approximation in Fq((T−1))Fq​((T−1))

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Quadratic approximation in $F_{q} ((T^{- 1}))$

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Quadratic approximation in $F_{q} ((T^{- 1}))$

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