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The number of exceptional approximations in Roth's theorem
Published online by Cambridge University Press: 09 April 2009
Abstract
Roth's Theorem says that given ρ < 2 and an algebraic number α, all but finitely many rational numbers x/y satisfy |α - (x/y)|< |y|-ρ. We give upper bounds for the number of these exceptional rationals when 3 ≤ ρ ≤ d, where d is the degree of α. Our result suplements bounds given by Bombieri and Van der Poorten when 2 > ρ ≤ 3; naturally the bounds become smaller as ρ increases.
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- Research Article
- Information
- Journal of the Australian Mathematical Society , Volume 59 , Issue 3 , December 1995 , pp. 375 - 383
- Copyright
- Copyright © Australian Mathematical Society 1995
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