Arithmetic theory of \(E\)-operators

DOI10.5802/jep.28zbMath1370.11090arXiv1406.5995OpenAlexW2150523887MaRDI QIDQ502550

Stéphane Fischler, Tanguy Rivoal

Publication date: 5 January 2017

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

Full work available at URL: https://arxiv.org/abs/1406.5995

zbMATH Keywords

Laplace transformasymptotic expansionspecial value\(E\)-operator\(G\)-operatorarithmetic Gevrey series

Mathematics Subject Classification ID

Transcendence theory of other special functions (11J91) Laplace transform (44A10) Other functions coming from differential, difference and integral equations (33E30) Stokes phenomena and connection problems (linear and nonlinear) for ordinary differential equations in the complex domain (34M40)

Related Items (10)

D-finite numbers ⋮ Values of \(E\)-functions are not Liouville numbers ⋮ Polynomial continued fractions for exp(π) ⋮ Minimization of differential equations and algebraic values of 𝐸-functions ⋮ On Siegel's problem for \(E\)-functions ⋮ Holomorphic solutions of \(E\)-operators ⋮ Linear independence of values of \(G\)-functions. II: Outside the disk of convergence ⋮ On the algebraic dependence ofE-functions ⋮ Regular extensions and algebraic relations between values of Mahler functions in positive characteristic ⋮ Siegel's problem for \(E\)-functions of order 2

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Matrices de Stokes et groupe de Galois des équations hypergéometriques confluentes generalisées. (Stokes matrices and Galois groups of generalized confluent hypergeometric equations)
• Rational approximations of values of the Gamma function on rationals
• 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
• On a continued fraction expansion for Euler's constant
• On the arithmetic nature of the values of the gamma function, Euler's constant, and Gompertz's constant
• A refined version of the Siegel-Shidlovskii theorem
• On the values of \(G\)-functions
• Euler’s constant: Euler’s work and modern developments
• RATIONAL APPROXIMATIONS TO VALUES OF BELL POLYNOMIALS AT POINTS INVOLVING EULER’S CONSTANT AND ZETA VALUES
• Rational approximations for values of derivatives of the Gamma function
• Algebraic values of G-functions.
• Microsolutions of differential operators and values of arithmetic Gevrey series
• On the Coefficients of Power Series Having Exponential Singularities
• A Short Proof of the Simple Continued Fraction Expansion of 𝑒
• On the Coefficients of Power Series having Exponential Singularities (Second Paper)

This page was built for publication: Arithmetic theory of \(E\)-operators