Strongly badly approximable matrices in fields of power series

2013/11/04 by Le, Thai Hoang, Vaaler, Jeffrey D.
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1311.0896

Abstract

We study the notion of strongly badly approximable matrices in the field of power series over 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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• Badly approximable systems of linear forms over a field of formal series
• Examples of badly approximable vectors over number fields
• Transference inequalities for multiplicative Diophantine exponents
• On badly approximable numbers
• Power iteration for matrices with power series entries