On Optimal Constants for Best Two-Dimensional Simultaneous Diophantine Approximations

 The main results of this paper state optimal constants for estimates of so-called successive minima in two dimensions under a constraint on the denominator. While these inequalities are known for every dimension, best possible constants within these estimates are, of course, notknown for any dimension larger than one and remain unknown for all dimensions larger than two. (Received 29 April 1998; in revised form 23 November 1998)