2019 •
On the Littlewood conjecture in fields of power series
Authors: Adamczewski, Boris, Bugeaud, Yann
Venue: Advanced Studies in Pure Mathematics
Type: Publication
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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