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

JOURNAL OF NUMBER THEORY

卷:105

Article

Tanaka, TA

关键词: algebraic independence;    Mahler functions;    Fibonacci numbers;    continued fractions;   

DOI  :  10.1016/j.jnt.2003.09.010

来源: Elsevier

【 摘 要 】

It is proved that the function Theta(z) = Sigma(kgreater than or equal to0) R-z(0)+R-1+(...)+R-k/(1-z(R0))(1-z(R1))(...)(1-z(Rk)), which can be expressed as a certain continued fraction certain continued fraction, takes algebraically independent values at any distinct nonzero algebraic numbers inside the unit circle if the sequence {R-k}(kgreater than or equal to0) is the generalized Fibonacci numbers. (C) 2003 Elsevier Inc. All rights reserved.

【 授权许可】

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