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Preprints, Working Papers, ... Year : 2005

On the Littlewood conjecture in fields of power series

Boris Adamczewski

Abstract

Let $\k$ be an arbitrary field. For any fixed badly approximable power series $\Theta$ in $\k((X^{-1}))$, 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.
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hal-00014580 , version 1 (28-11-2005)

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Boris Adamczewski, Yann Bugeaud. On the Littlewood conjecture in fields of power series. 2005. ⟨hal-00014580⟩
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