Details

Autor(en) / Beteiligte

• Ghosh, Anish
• Gorodnik, Alexander
• Nevo, Amos

Titel

Metric Diophantine approximation on homogeneous varieties

Ist Teil von

• Compositio mathematica, 2014-08, Vol.150 (8), p.1435-1456

Ort / Verlag

London, UK: London Mathematical Society

Erscheinungsjahr

2014

Link zum Volltext

Quelle

Electronic Journals Library - Freely accessible e-journals

Beschreibungen/Notizen

• 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 $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}S$-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.