Diophantine approximation with restricted numerators and denominators on semisimple groups

TL;DR

This paper investigates Diophantine approximation on semisimple algebraic groups, providing quantitative results for approximating real points with rational points that have prescribed denominators and almost prime numerators.

Contribution

It introduces a new approach to Diophantine approximation on semisimple groups with restrictions on numerators and denominators, achieving quantitative approximation results.

Findings

Established a quantitative approximation theorem for real points by rational points with prescribed denominators.

Proved approximation with almost prime numerators in semisimple algebraic groups.

Extended Diophantine approximation theory to restricted rational points on algebraic groups.

Abstract

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 any prescribed denominator and an almost prime numerator.