Diophantine approximation on matrices and Lie groups
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Date
2018-02
Publication Type
Journal Article
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yes
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Abstract
We study the general problem of extremality for metric diophantine approximation on submanifolds of matrices. We formulate a criterion for extremality in terms of a certain family of algebraic obstructions and show that it is sharp. In general the almost sure diophantine exponent of a submanifold is shown to depend only on its Zariski closure, and when the latter is defined over Q, we prove that the exponent is rational and give a method to effectively compute it. This method is applied to a number of cases of interest. In particular we prove that the diophantine exponent of rational nilpotent Lie groups exists and is a rational number, which we determine explicitly in terms of representation theoretic data.
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published
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Journal / series
Volume
28 (1)
Pages / Article No.
1 - 57
Publisher
Birkhäuser
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Subject
Metric diophantine approximation; Homogeneous dynamics; Extremal manifolds; Group actions
Organisational unit
03826 - Einsiedler, Manfred L. / Einsiedler, Manfred L.
Notes
Funding
152819 - Equidistribution and dynamics on homogeneous spaces (SNF)