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On the Littlewood conjecture in fields of power series

Boris Adamczewski·Yann Bugeaud
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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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Boris Adamczewski, Yann Bugeaud. 2005-11-28. On the Littlewood conjecture in fields of power series. https://arxiv.org/abs/math/0511680

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