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Diophantine approximation with restricted numerators and denominators on semisimple groups. (English. French summary) Zbl 1429.11125

Summary: We consider the problem of Diophantine approximation on semisimple algebraic groups by rational points with restricted numerators and denominators and establish a quantitative approximation result for all real points in the group by rational points with a prescribed denominator and an almost prime numerator.

MSC:

11J25 Diophantine inequalities
11N25 Distribution of integers with specified multiplicative constraints
11N36 Applications of sieve methods
20G30 Linear algebraic groups over global fields and their integers
22E30 Analysis on real and complex Lie groups
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