On the Littlewood conjecture in fields of power series

Boris Adamczewski; Yann Bugeaud

On the Littlewood conjecture in fields of power series

Number Theory 2012-05-07 v1

Authors: Boris Adamczewski , Yann Bugeaud

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.

Keywords

littlewood conjecture power series badly approximable fields of formal laurent series algebraic power series

Cite

@article{arxiv.math/0511680,
  title  = {On the Littlewood conjecture in fields of power series},
  author = {Boris Adamczewski and Yann Bugeaud},
  journal= {arXiv preprint arXiv:math/0511680},
  year   = {2012}
}

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