Metric Diophantine approximation on homogeneous varieties

Ghosh, Anish ; Gorodnik, Alexander ; Nevo, Amos (2014) Metric Diophantine approximation on homogeneous varieties Compositio Mathematica, 150 (08). pp. 1435-1456. ISSN 0010-437X

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We develop the metric theory of Diophantine approximation on homogeneous varieties of semisimple algebraic groups and prove results analogous to the classical Khintchine and Jarník theorems. In full generality our results establish simultaneous Diophantine approximation with respect to several completions, and Diophantine approximation over general number fields using S-algebraic integers. In several important examples, the metric results we obtain are optimal. The proof uses quantitative equidistribution properties of suitable averaging operators, which are derived from spectral bounds in automorphic representations.

Item Type:Article
Source:Copyright of this article belongs to Cambridge University Press.
Keywords:37A17; 11K60 (Primary)
ID Code:114435
Deposited On:05 Jun 2018 07:02
Last Modified:05 Jun 2018 07:02

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