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VOL. 49 | 2007 On the Littlewood conjecture in fields of power series
Boris Adamczewski, Yann Bugeaud

Editor(s) Shigeki Akiyama, Kohji Matsumoto, Leo Murata, Hiroshi Sugita

Abstract

Let $\mathbf{k}$ be an arbitrary field. For any fixed badly approximable power series $\Theta$ in $\mathbf{k}((X^{-1}))$, we give an explicit construction of continuum many badly approximable power series $\Phi$ for which the pair $(\Theta, \Phi)$ satisfies the Littlewood conjecture. We further discuss the Littlewood conjecture for pairs of algebraic power series.

Information

Published: 1 January 2007
First available in Project Euclid: 27 January 2019

zbMATH: 1223.11083
MathSciNet: MR2405595

Digital Object Identifier: 10.2969/aspm/04910001

Subjects:
Primary: 11J13
Secondary: 11J61

Rights: Copyright © 2007 Mathematical Society of Japan

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