For all m,n with m+n>2 and any norms, the set of possible asymptotic Dirichlet approximation errors is exactly [0,Delta], with every value attained densely and uncountably often.
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The Dirichlet spectrum
For all m,n with m+n>2 and any norms, the set of possible asymptotic Dirichlet approximation errors is exactly [0,Delta], with every value attained densely and uncountably often.