Algebraic independence of Mahler functions and their values

DOI10.2748/tmj/1178225412zbMath0852.11036OpenAlexW1987467476MaRDI QIDQ1915241

Kumiko Nishioka

Publication date: 5 December 1996

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2748/tmj/1178225412

zbMATH Keywords

algebraic independenceMahler functions in several complex variables

Mathematics Subject Classification ID

Algebraic independence; Gel'fond's method (11J85) Functional equations for complex functions (39B32)

Related Items (12)

Algebraic independence of certain entire functions of two variables generated by linear recurrences ⋮ Algebraic independence of the values of functions satisfying Mahler type functional equations under the transformation represented by a power relatively prime to the characteristic of the base field ⋮ A new proof of Nishioka's theorem in Mahler's method ⋮ Algebraic independence of the partial derivatives of certain functions with arbitrary number of variables ⋮ Algebraic independence of the values of power series and their derivatives generated by linear recurrences ⋮ Algebraic independence results for a certain family of power series, infinite products, and Lambert type series ⋮ Algebraic independence results for the values of certain Mahler functions and their application to infinite products ⋮ Algebraic independence of reciprocal sums of binary recurrences ⋮ Unnamed Item ⋮ Algebraic independence of the values of the Hecke–Mahler series and its derivatives at algebraic numbers ⋮ Mahler's method ⋮ Algebraic independence of the values of certain series and their derivatives involving the Hecke-Mahler series

Cites Work

• Unnamed Item
• Unnamed Item
• Algebraic independence of certain power series of algebraic numbers
• A vanishing theorem for power series
• On the algebraic independence of holomorphic solutions of certain functional equations and their values
• A class of hypertranscendental functions
• Note on a paper by Mahler
• An axiomatization of Nesterenko's method and applications on Mahler functions
• New approach in Mahler's method.

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