Algebraic theory of difference equations and Mahler functions

Kumiko Nishioka; Seiji Nishioka

doi:10.1007/s00010-012-0132-3

Algebraic theory of difference equations and Mahler functions

Kumiko Nishioka, Seiji Nishioka

Department of Economic

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

Algebraic independence of certain Mahler functions constructed from Rudin-Schapiro sequences and Baum-Sweet sequences is proved, using difference Riccati equations and the notion of difference field extension of valuation ring type.

Original language	English
Pages (from-to)	245-259
Number of pages	15
Journal	Aequationes Mathematicae
Volume	84
Issue number	3
DOIs	https://doi.org/10.1007/s00010-012-0132-3
Publication status	Published - 2012 Dec

Keywords

Mahler function
algebraic independence
difference algebra
transcendence

ASJC Scopus subject areas

Mathematics(all)
Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1007/s00010-012-0132-3

Cite this

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title = "Algebraic theory of difference equations and Mahler functions",

abstract = "Algebraic independence of certain Mahler functions constructed from Rudin-Schapiro sequences and Baum-Sweet sequences is proved, using difference Riccati equations and the notion of difference field extension of valuation ring type.",

keywords = "Mahler function, algebraic independence, difference algebra, transcendence",

author = "Kumiko Nishioka and Seiji Nishioka",

note = "Funding Information: The second author is supported by JSPS Research Fellowships for Young Scientists, by KAKENHI (20 · 4941) and by KAKENHI (23 · 5166).",

year = "2012",

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doi = "10.1007/s00010-012-0132-3",

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AU - Nishioka, Kumiko

AU - Nishioka, Seiji

N1 - Funding Information: The second author is supported by JSPS Research Fellowships for Young Scientists, by KAKENHI (20 · 4941) and by KAKENHI (23 · 5166).

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Y1 - 2012/12

N2 - Algebraic independence of certain Mahler functions constructed from Rudin-Schapiro sequences and Baum-Sweet sequences is proved, using difference Riccati equations and the notion of difference field extension of valuation ring type.

AB - Algebraic independence of certain Mahler functions constructed from Rudin-Schapiro sequences and Baum-Sweet sequences is proved, using difference Riccati equations and the notion of difference field extension of valuation ring type.

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KW - algebraic independence

KW - difference algebra

KW - transcendence

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Algebraic theory of difference equations and Mahler functions

Abstract

Keywords

ASJC Scopus subject areas

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