2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/174050We refine Khintchine Transference Principle which relates the measure of simultaneous rational approximation of an $n$ real numbers with the measure of linear independence of these $n$ numbers. Khintchine's inequalities are known to be optimal. However, they may be sharpened by taking into account two further uniform exponents.Number Theory11J13text