Dirichlet spectrum for one linear form

For n ⩾ 2 $n\geqslant 2$ , we determine the Dirichlet spectrum in R $\mathbb {R}^n$ with respect to a linear form and maximum norm as entire interval [0, 1]. This natural result improves on recent work of Beresnevich et al. complements subsequent paper by authors where analogous was proved for simultaneous approximation. Various generalizations that can be obtained similar methods latter are indicated. We believe our results an important step toward resolving very open problem general system forms.