Algebraic independence of the values of Mahler functions associated with a certain continued fraction expansion

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2 Citations (Scopus)

Abstract

It is proved that the function (a formula is presented), which can be expressed as a certain continued fraction, takes algebraically independent values at any distinct nonzero algebraic numbers inside the unit circle if the sequence {Rk}k≥0 is the generalized Fibonacci numbers.

Original languageEnglish
Pages (from-to)38-48
Number of pages11
JournalJournal of Number Theory
Volume105
Issue number1
DOIs
Publication statusPublished - 2004 Mar

Fingerprint

Generalized Fibonacci numbers
Algebraic Independence
Continued Fraction Expansion
Algebraic number
Continued fraction
Unit circle
Distinct

Keywords

  • Algebraic independence
  • Continued fractions
  • Fibonacci numbers
  • Mahler functions

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

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title = "Algebraic independence of the values of Mahler functions associated with a certain continued fraction expansion",
abstract = "It is proved that the function (a formula is presented), which can be expressed as a certain continued fraction, takes algebraically independent values at any distinct nonzero algebraic numbers inside the unit circle if the sequence {Rk}k≥0 is the generalized Fibonacci numbers.",
keywords = "Algebraic independence, Continued fractions, Fibonacci numbers, Mahler functions",
author = "Takaaki Tanaka",
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