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Some inequalities for diophantine approximation by continued fractions
Published online by Cambridge University Press: 17 April 2009
Abstract
Let ξ be an irrational number with simple continued fraction expansion ξ = [a0;a1,a2,…,an,…], let pn/qn be its nth convergent and let θn = qn|qnξ − pn|. In this paper a general method is introduced to deduce a series of inequalities involving the triple (θn−1, θn, θn+1).
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- Copyright © Australian Mathematical Society 1990