scholarly journals Algebraic independence of mahler functions and their values

Author(s):  
Kumiko Nishioka
2016 ◽  
Vol 12 (08) ◽  
pp. 2159-2166
Author(s):  
Keijo Väänänen

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.


Author(s):  
Richard P. Brent ◽  
Michael Coons ◽  
Wadim Zudilin

2014 ◽  
Vol 98 (3) ◽  
pp. 289-310 ◽  
Author(s):  
PETER BUNDSCHUH ◽  
KEIJO VÄÄNÄNEN

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.


2000 ◽  
Vol 75 (2) ◽  
pp. 121-124 ◽  
Author(s):  
B. Greuel

2018 ◽  
Vol 111 (2) ◽  
pp. 145-155
Author(s):  
Masaaki Amou ◽  
Keijo Väänänen

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