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

被引：2

作者：

Tanaka, TA ^{[1
]}

机构：

[1] Keio Univ, Dept Math, Kohoku Ku, Yokohama, Kanagawa 2238522, Japan

来源：

JOURNAL OF NUMBER THEORY | 2004年 / 105卷 / 01期

关键词：

algebraic independence; Mahler functions; Fibonacci numbers; continued fractions;

D O I：

10.1016/j.jnt.2003.09.010

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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.

引用

页码：38 / 48

页数：11

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