Algebraic independence of the values of certain series by Mahler's method

1992 ◽  
Vol 114 (3-4) ◽  
pp. 183-198 ◽  
Author(s):  
Paul-Georg Becker
Keyword(s):  
Algebraic Independence ◽  
Mahler’S Method ◽  
Mahler's Method

Transcendental Numbers Arising from Mahler’s Method

2021 ◽  
pp. 111-120
Author(s):  
Saeree Wananiyakul ◽  
Vichian Laohakosol ◽  
Janyarak Tongsomporn
Keyword(s):  
Transcendental Numbers ◽  
Mahler’S Method ◽  
Mahler's Method

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 Independance algebrique des derivees d'une periode du module de Carlitz

2000 ◽  
Vol 69 (1) ◽  
pp. 8-18 ◽  
Author(s):  
Laurent Denis
Keyword(s):  
Fundamental Period ◽  
Mahler’S Method ◽  
Mahler's Method ◽  
Derivatives Of

AbstractWe prove here that the p - 1 first derivatives of the fundamental period of the Carliz module are algebraically independent. For that purpose we will show to use Mahler's method in this situtaion.

Algebraic Independence Results Related to 〈q, r〉-Number Systems

2006 ◽  
Vol 147 (4) ◽  
pp. 319-335 ◽  
Author(s):  
Shin-ichiro Okada ◽  
Iekata Shiokawa
Keyword(s):  
Algebraic Independence ◽  
Number Systems ◽  
Independence Results
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