On the values of \(G\)-functions

DOI10.4171/CMH/321zbMath1304.11070arXiv1103.6022OpenAlexW4327757882MaRDI QIDQ2510750

Tanguy Rivoal, Stéphane Fischler

Publication date: 4 August 2014

Published in: Commentarii Mathematici Helvetici (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1103.6022

zbMATH Keywords

rational approximationlinear differential equationperiod\(G\)-functionsingularity analysis

Mathematics Subject Classification ID

Transcendence theory of other special functions (11J91) Other functions coming from differential, difference and integral equations (33E30) Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35) Stokes phenomena and connection problems (linear and nonlinear) for ordinary differential equations in the complex domain (34M40)

Related Items (16)

D-finite numbers ⋮ Linear independence of values of \(G\)-functions ⋮ Values of \(E\)-functions are not Liouville numbers ⋮ Polynomial continued fractions for exp(π) ⋮ Minimization of differential equations and algebraic values of 𝐸-functions ⋮ Rational approximation to values of \(G\)-functions, and their expansions in integer bases ⋮ On Siegel's problem for \(E\)-functions ⋮ Values of globally bounded $G$-functions ⋮ Arithmetic theory of \(E\)-operators ⋮ ON THE DENOMINATORS OF THE TAYLOR COEFFICIENTS OF <i>G</i>-FUNCTIONS ⋮ Linear independence of values of \(G\)-functions. II: Outside the disk of convergence ⋮ Counting walks with large steps in an orthant ⋮ Euler’s constant: Euler’s work and modern developments ⋮ On the equality of periods of Kontsevich-Zagier ⋮ A semi-canonical reduction for periods of Kontsevich–Zagier ⋮ Padé approximation for a class of hypergeometric functions and parametric geometry of numbers

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