Restricted rational approximation and Apéry-type constructions

DOI10.1016/S0019-3577(09)00020-2zbMath1198.11057MaRDI QIDQ963237

Stéphane Fischler

Publication date: 8 April 2010

Published in: Indagationes Mathematicae. New Series (Search for Journal in Brave)

zbMATH Keywords

Hausdorff dimensionexponent of irrationalityrestricted rational approximation

Mathematics Subject Classification ID

Measures of irrationality and of transcendence (11J82) Approximation by numbers from a fixed field (11J17)

Related Items (4)

Quantitative generalizations of Nesterenkos's linear independence criterion ⋮ Irrationality exponent and rational approximations with prescribed growth ⋮ On simultaneous Diophantine approximations to \(\zeta(2)\) and \(\zeta(3)\) ⋮ Nesterenko's criterion when the small linear forms oscillate

Cites Work

• Convergents and irrationality measures of logarithms
• A refinement of Nesterenko's linear independence criterion with applications to zeta values
• Resurrecting the asymptotics of linear recurrences
• A proof that Euler missed. Apéry's proof of the irrationality of \(\zeta(3)\). An informal report
• On a property of Pisot numbers and related questions
• A few remarks on \(\zeta (3)\)
• An asymptotic formula for binomial sums
• On approximation of some logarithms of rational numbers by rational fractions of special type
• The group structure for ζ(3)
• Un exposant de densite en approximation rationnelle
• Irrationality exponent and rational approximations with prescribed growth
• The Hausdorff dimension of certain sets arising from Diophantine approximation by restricted sequences of integer vectors
• A new irrationality measure for ζ(3)
• Rational approximations to algebraic numbers
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