Simultaneous diophantine approximations and cubic irrationals

William Wells Adams

Vol. 30 (1969), No. 1, 1–14

DOI: 10.2140/pjm.1969.30.1

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 β₁,β₂ there is an infinity of rational integers q > 0,p₁,p₂ satisfying

Mathematical Subject Classification

Primary: 10.31

Milestones

Received: 28 October 1968

Published: 1 July 1969