Dirichlet's approximation theorem: Difference between revisions

Revision as of 17:31, 5 February 2010

Revision as of 17:32, 5 February 2010

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:<math> \left| \alpha -\frac{p}{q} \right| < \frac{1}{q^2} </math>

is satisfied by infinitely many integers ''p'' and ''q''. This corollary also shows that the [[Thue–Siegel–Roth theorem]], a result in the other direction, provides essentially the tightest possible bound, in the sense that the limits on rational approximation of [[algebraic number]]s cannot be improved by lowering the exponent 2 + &epsilon; beyond 2.

==Method of proof==