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2005 • On the Littlewood conjecture in fields of power series

Authors: Boris Adamczewski, Yann Bugeaud

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.

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On the Littlewood conjecture in fields of power series

Boris Adamczewski, Yann Bugeaud

N/A · 2007

N/A

Open Access

Article

Missing works

10.2969/aspm/04910001

10.48550/arxiv.math/0511680