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Multiplicatively badly approximable matrices in fields of power series


Authors: Thái Hoàng Lê and Jeffrey D. Vaaler
Journal: Proc. Amer. Math. Soc. 143 (2015), 3791-3800
MSC (2010): Primary 11J13, 11T55
DOI: https://doi.org/10.1090/S0002-9939-2015-12570-1
Published electronically: March 25, 2015
MathSciNet review: 3359571
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Abstract: We study the notion of multiplicatively badly approximable matrices in the field of a Laurent series with coefficients in a field $ K$. We prove a transference principle in this setting, and show that such matrices exist when $ K$ is infinite.


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Additional Information

Thái Hoàng Lê
Affiliation: Department of Mathematics, The University of Texas at Austin, 1 University Station, C1200, Austin, Texas 78712
Email: leth@math.utexas.edu

Jeffrey D. Vaaler
Affiliation: Department of Mathematics, The University of Texas at Austin, 1 University Station, C1200, Austin, Texas 78712
Email: vaaler@math.utexas.edu

DOI: https://doi.org/10.1090/S0002-9939-2015-12570-1
Keywords: Linear forms, fractional part, Littlewood conjecture
Received by editor(s): October 30, 2013
Received by editor(s) in revised form: May 31, 2014
Published electronically: March 25, 2015
Additional Notes: The research of the second author was supported by NSA grant, H98230-12-1-0254.
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2015 American Mathematical Society

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