A CRITERION FOR THE ALGEBRAIC INDEPENDENCE OF VALUES OF A CLASS OF HYPERGEOMETRIC $ E$-FUNCTIONS

DOI10.1070/SM1991V069N01ABEH002113zbMath0712.11044OpenAlexW2061549017MaRDI QIDQ3497153

V. Kh. Salikhov

Publication date: 1991

Published in: Mathematics of the USSR-Sbornik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1070/sm1991v069n01abeh002113

zbMATH Keywords

irreducibilityalgebraic differential equationSiegel E-function

Mathematics Subject Classification ID

Algebraic independence; Gel'fond's method (11J85) Transcendence theory of other special functions (11J91) Transcendence (general theory) (11J81) Differential algebra (12H05) General theory for ordinary differential equations (34A99)

Related Items (9)

On the algebraic properties of solutions of inhomogeneous hypergeometric equations ⋮ Arithmetic properties of the values of generalized hypergeometric series with polyadic transcendental parameters ⋮ Transcendence of \(p\)-adic values of generalized hypergeometric series with transcendental polyadic parameters ⋮ Arithmetic properties of values at polyadic Liouville points of Euler-type series with polyadic Liouville parameter ⋮ Arithmetic properties of an Euler-type series with polyadic Liouville parameter ⋮ Arithmetic properties of Euler-type series with a Liouvillian polyadic parameter ⋮ Arithmetic properties of generalized hypergeometric \(F\)-series ⋮ New problems in the theory of transcendental polyadic numbers ⋮ Product formula, global relations, and polyadic numbers

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