Improved constants for effective irrationality measures from hypergeometric functions

DOI10.2140/moscow.2022.11.161zbMath1501.11078arXiv2111.01044OpenAlexW3210341786WikidataQ113727169 ScholiaQ113727169MaRDI QIDQ2165898

Paul M. Voutier

Publication date: 23 August 2022

Published in: Moscow Journal of Combinatorics and Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2111.01044

zbMATH Keywords

hypergeometric functionsDiophantine approximationeffective irrationality measure exponent

Mathematics Subject Classification ID

Measures of irrationality and of transcendence (11J82) Classical hypergeometric functions, ({}_2F_1) (33C05) Approximation to algebraic numbers (11J68)

Cites Work

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• Explicit bounds for primes in arithmetic progressions
• Complete solution of the diophantine equation \(X^ 2+1=dY^ 4\) and a related family of quartic Thue equations
• Thue's fundamental theorem. II: Further refinements and examples
• On the method of Thue-Siegel
• Number theory IV: Transcendental numbers. Transl. from the Russian by N. Koblitz
• Approximate formulas for some functions of prime numbers
• Rational approximations to \(\root 3\of 2\) and other algebraic numbers revisited
• Rational approximation to algebraic numbers of small height: the Diophantine equation |axn - byn|= 1
• Effective irrationality measures and approximation by algebraic conjugates
• Thue's Fundamentaltheorem, I: The general case
• RATIONAL APPROXIMATIONS TO 23 AND OTHER ALGEBRAIC NUMBERS