scholarly journals Algebraic independence of mahler functions and their values

1996 ◽  
pp. 78-117
Author(s):  
Kumiko Nishioka
Keyword(s):  
Algebraic Independence ◽  
Mahler Functions

scholarly journals Algebraic independence of certain Mahler numbers

2016 ◽  
Vol 12 (08) ◽  
pp. 2159-2166
Author(s):  
Keijo Väänänen
Keyword(s):  
Unit Disk ◽  
Generating Functions ◽  
Special Class ◽  
Algebraic Independence ◽  
Open Unit ◽  
Open Unit Disk ◽  
Algebraic Point ◽  
Mahler’S Method ◽  
Mahler Functions ◽  
Independence Results

In this note, we prove algebraic independence results for the values of a special class of Mahler functions. In particular, the generating functions of Thue–Morse, regular paperfolding and Cantor sequences belong to this class, and we obtain the algebraic independence of the values of these functions at every non-zero algebraic point in the open unit disk. The proof uses results on Mahler's method.

scholarly journals Algebraic Independence of Mahler Functions via Radial Asymptotics

2015 ◽  
pp. rnv139 ◽  
Author(s):  
Richard P. Brent ◽  
Michael Coons ◽  
Wadim Zudilin
Keyword(s):  
Algebraic Independence ◽  
Mahler Functions

ALGEBRAIC INDEPENDENCE OF CERTAIN MAHLER FUNCTIONS AND OF THEIR VALUES

2014 ◽  
Vol 98 (3) ◽  
pp. 289-310 ◽  
Author(s):  
PETER BUNDSCHUH ◽  
KEIJO VÄÄNÄNEN
Keyword(s):  
Rational Function ◽  
Complex Number ◽  
Functional Equations ◽  
Algebraic Independence ◽  
Lucas Numbers ◽  
Mahler Functions ◽  
Independence Results ◽  
Nonzero Complex Number ◽  
Fibonacci And Lucas Numbers ◽  
Reciprocal Sums

This paper considers algebraic independence and hypertranscendence of functions satisfying Mahler-type functional equations $af(z^{r})=f(z)+R(z)$, where $a$ is a nonzero complex number, $r$ an integer greater than 1, and $R(z)$ a rational function. Well-known results from the scope of Mahler’s method then imply algebraic independence over the rationals of the values of these functions at algebraic points. As an application, algebraic independence results on reciprocal sums of Fibonacci and Lucas numbers are obtained.

Algebraic independence of Mahler functions

2000 ◽  
Vol 75 (2) ◽  
pp. 121-124 ◽  
Author(s):  
B. Greuel
Keyword(s):  
Algebraic Independence ◽  
Mahler Functions

scholarly journals Algebraic independence of certain Mahler functions

2018 ◽  
Vol 111 (2) ◽  
pp. 145-155
Author(s):  
Masaaki Amou ◽  
Keijo Väänänen
Keyword(s):  
Algebraic Independence ◽  
Mahler Functions
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