Values of \(E\)-functions are not Liouville numbers

DOI10.5802/jep.249arXiv2301.01158MaRDI QIDQ6122615

Tanguy Rivoal, Stéphane Fischler

Publication date: 1 March 2024

Published in: Journal de l'École Polytechnique -- Mathématiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2301.01158

zbMATH Keywords

transcendence measures\(E\)-functionsLiouville numbersirrationality measureslinear independence measuresAndré-Beukers theoremsShidlovskii's theorem

Mathematics Subject Classification ID

Transcendence theory of other special functions (11J91) Measures of irrationality and of transcendence (11J82)

Cites Work

• Arithmetic theory of \(E\)-operators
• Number theory IV: Transcendental numbers. Edited by A. N. Parshin, I. R. Shafarevich and R. V. Gamkrelidze. Transl. from the Russian by Neal Koblitz
• Gevrey series of arithmetic type. I: Purity and duality theorems
• Transcendental numbers. With a foreword by W. Dale Brownawell. Transl. from the Russian by Neal Koblitz
• Effective estimates for global relations on Euler-type series
• A refined version of the Siegel-Shidlovskii theorem
• On the values of \(G\)-functions
• Diophantine properties of real numbers generated by finite automata
• Équations différentielles linéaires et majorations de multiplicités
• Linear independence of values of $ E$-functions
• Microsolutions of differential operators and values of arithmetic Gevrey series
• On rational approximations of values of a certain class of entire functions
• Diophantine approximation of Mahler numbers
• Méthode de Mahler : relations linéaires, transcendance et applications aux nombres automatiques
• Solution algebras of differential equations and quasi-homogeneous varieties: a new differential Galois correspondence
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