Metric Diophantine approximation on homogeneous varieties

Anish Ghosh*, Alexander Gorodnik (Gorodnyk), Amos Nevo

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)

5 Citations (Scopus)
265 Downloads (Pure)

Abstract

We develop the metric theory of Diophantine approximation on homogeneous varieties of semisimple algebraic groups and prove results analogous to the classical Khinchin and Jarnik 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.
Original languageEnglish
Pages (from-to)1435-1456
Number of pages22
JournalCompositio Mathematica
Volume150
Issue number8
Early online date20 Jun 2014
DOIs
Publication statusPublished - Aug 2014

Keywords

  • automorphic spectrum
  • Diophantine approximation
  • homogeneous varieties
  • Jarník theorem
  • Khintchine theorem
  • semisimple algebraic groups

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