On exponents of homogeneous and inhomogeneous Diophantine approximation

In Diophantine Approximation, inhomogeneous problems are linked with homogeneous ones by means of the so-called Transference Theorems. We revisit this classical topic by introducing new exponents of Diophantine approximation. We prove that the inhomogeneous exponent of approximation to a generic point in $\mathbb R^n$ by a system of $n$ linear forms is equal to the inverse of the uniform homogeneous exponent associated to the system of dual linear forms.