### 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 {R_{k}}_{k≥0} is the generalized Fibonacci numbers.

Original language | English |
---|---|

Pages (from-to) | 38-48 |

Number of pages | 11 |

Journal | Journal of Number Theory |

Volume | 105 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2004 Mar |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

**Algebraic independence of the values of Mahler functions associated with a certain continued fraction expansion.** / Tanaka, Takaaki.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Algebraic independence of the values of Mahler functions associated with a certain continued fraction expansion

AU - Tanaka, Takaaki

PY - 2004/3

Y1 - 2004/3

N2 - 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.

AB - 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.

KW - Algebraic independence

KW - Continued fractions

KW - Fibonacci numbers

KW - Mahler functions

UR - http://www.scopus.com/inward/record.url?scp=1342263871&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1342263871&partnerID=8YFLogxK

U2 - 10.1016/j.jnt.2003.09.010

DO - 10.1016/j.jnt.2003.09.010

M3 - Article

AN - SCOPUS:1342263871

VL - 105

SP - 38

EP - 48

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

IS - 1

ER -