Anish Ghosh, Alexander Gorodnik, Amos Nevo
Published 2010-07-04Version 1
The present paper establishes qunatitative estimates on the rate of diophantine approximation in homogeneous varieties of semisimple algebraic groups. The estimates established generalize and improve previous ones, and are sharp in a number of cases. We show that the rate of diophantine approximation is controlled by the spectrum of the automorphic representation, and is thus subject to the generalised Ramanujan conjectures.
Diophantine approximation on lines with prime constraints
Exponents of diophantine approximation in dimension $2$ for numbers of Sturmian type
Systems of small linear forms and Diophantine approximation on manifolds
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