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.
- Almost primes
- Diophantine approximation in algebraic groups
- Property (τ)
- Restricted diophantine approximation
- Sieving on algebraic groups