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January 2017 Quadratic approximation in $\mathbb{F}_q(\!(T^{-1})\!)$
Tomohiro Ooto
Osaka J. Math. 54(1): 129-156 (January 2017).

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. "Quadratic approximation in $\mathbb{F}_q(\!(T^{-1})\!)$." Osaka J. Math. 54 (1) 129 - 156, January 2017.

Information

Published: January 2017
First available in Project Euclid: 3 March 2017

zbMATH: 1381.11058
MathSciNet: MR3619752

Subjects:
Primary: 11J61
Secondary: 11J70 , 11J82

Rights: Copyright © 2017 Osaka University and Osaka City University, Departments of Mathematics

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Vol.54 • No. 1 • January 2017
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