Diophantine approximation and automorphic spectrum

Details Diophantine approximation and automorphic spectrum Diophantine approximation and automorphic spectrum

2010-07-04

arxiv.org/abs/1007.0593v1

Mathematics

Number Theory

Scientific paper

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.

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