We 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.
Note on the spectrum of classical and uniform exponents of Diophantine approximation
On transfer inequalities in Diophantine approximation
Diophantine approximation on manifolds and lower bounds for Hausdorff dimension
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