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

Taka Aki Tanaka

doi:10.1016/j.jnt.2003.09.010

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

Taka Aki Tanaka

Department of Mathematics

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

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 {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	https://doi.org/10.1016/j.jnt.2003.09.010
Publication status	Published - 2004 Mar

Keywords

Algebraic independence
Continued fractions
Fibonacci numbers
Mahler functions

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1016/j.jnt.2003.09.010

Cite this

@article{00aed998ab98480284e5be9a67d14594,

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 = "Tanaka, {Taka Aki}",

year = "2004",

month = mar,

doi = "10.1016/j.jnt.2003.09.010",

language = "English",

volume = "105",

pages = "38--48",

journal = "Journal of Number Theory",

issn = "0022-314X",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

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

AU - Tanaka, Taka Aki

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

SN - 0022-314X

VL - 105

SP - 38

EP - 48

JO - Journal of Number Theory

JF - Journal of Number Theory

IS - 1

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this