Exceptional values of E-functions at algebraic points

DOI10.1112/blms.12168zbMath1450.11076arXiv1708.00217OpenAlexW2963258887MaRDI QIDQ4583636

Tanguy Rivoal, Boris Adamczewski

Publication date: 31 August 2018

Published in: Bulletin of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1708.00217

zbMATH Keywords

algebraic independenceSiegel-Shidlovskiĭ theorem

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Transcendence theory of other special functions (11J91) Other functions coming from differential, difference and integral equations (33E30) Transcendence (general theory) (11J81) Entire and meromorphic solutions to ordinary differential equations in the complex domain (34M05)

Related Items (10)

Factors of \(E\)-operators with an \(\eta\)-apparent singularity at zero ⋮ Entire functions with undecidable arithmetic properties ⋮ Effective algebraic independence of values of \(E\)-functions ⋮ Minimization of differential equations and algebraic values of 𝐸-functions ⋮ Méthode de Mahler en caractéristique non nulle : un analogue du théorème de Ku. Nishioka ⋮ Algebraic properties of Э-functions ⋮ Linear independence of values of \(G\)-functions. II: Outside the disk of convergence ⋮ Regular extensions and algebraic relations between values of Mahler functions in positive characteristic ⋮ Explicit degree bounds for right factors of linear differential operators ⋮ Undecidable arithmetic properties of solutions of Fredholm integral equations

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