Algebraic independence of the power series defined by blocks of digits

DOI10.1006/jnth.1999.2399zbMath0934.11036OpenAlexW1973088652MaRDI QIDQ1306700

Yoshihisa Uchida

Publication date: 26 April 2000

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jnth.1999.2399

zbMATH Keywords

transcendencepower seriesalgebraic independenceblock of digitsnumber of occurrencesbase \(q\) expansionpatterns of digits

Mathematics Subject Classification ID

Algebraic independence; Gel'fond's method (11J85) Transcendence (general theory) (11J81) Automata sequences (11B85)

Related Items (5)

Algebraic theory of difference equations and Mahler functions ⋮ Linear relations between pattern sequences in a \(\langle q, r\rangle\)-numeration system ⋮ Algebraic independence results related to pattern sequences in distinct \(\langle q,r \rangle\)-numeration systems ⋮ Pattern sequences in \(\langle q,r\rangle\)-numeration systems ⋮ \(q\)-linear functions and algebraic independence.

Cites Work

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• The ring of \(k\)-regular sequences
• On the algebraic independence of holomorphic solutions of certain functional equations and their values
• A class of hypertranscendental functions
• \(k\)-regular power series and Mahler-type functional equations
• Mahler functions and transcendence
• Paper Folding, Digit Patterns and Groups of Arithmetic Fractals
• New approach in Mahler's method.
• Infinite Products Associated with Counting Blocks in Binary Strings

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