On the Littlewood conjecture in fields of power series

Details On the Littlewood conjecture in fields of power series On the Littlewood conjecture in fields of power series

2005-11-28

arxiv.org/abs/math/0511680v1

Mathematics

Number Theory

Scientific paper

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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