Vol. 30, No. 1, 1969

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ISSN: 0030-8730
Simultaneous diophantine approximations and cubic irrationals

William Wells Adams

Vol. 30 (1969), No. 1, 1–14
Abstract

The purpose of this paper is to make some remarks concerning the best order of approximation in two-dimensional simultaneous diophantine approximations. That is, let c0 be the infimum over all constants c > 0 such that for every pair of real numbers β12 there is an infinity of rational integers q > 0,p1,p2 satisfying

(∗)|qβ1 − p1| < (c′lq)1∕2,|qβ2 − p2| < (c∕q)1∕2.

Mathematical Subject Classification
Primary: 10.31
Milestones
Received: 28 October 1968
Published: 1 July 1969
Authors
William Wells Adams