Algebraic independence results for reciprocal sums of Fibonacci numbers

2011 ◽  
Vol 148 (3) ◽  
pp. 205-223 ◽  
Author(s):  
Carsten Elsner ◽  
Shun Shimomura ◽  
Iekata Shiokawa
Keyword(s):  
Fibonacci Numbers ◽  
Algebraic Independence ◽  
Independence Results ◽  
Reciprocal Sums

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 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

scholarly journals Algebraic relations for reciprocal sums of Fibonacci numbers

2007 ◽  
Vol 130 (1) ◽  
pp. 37-60 ◽  
Author(s):  
Carsten Elsner ◽  
Shun Shimomura ◽  
Iekata Shiokawa
Keyword(s):  
Fibonacci Numbers ◽  
Reciprocal Sums

scholarly journals Transcendence of Rogers-Ramanujan continued fraction and reciprocal sums of Fibonacci numbers

1997 ◽  
Vol 73 (7) ◽  
pp. 140-142 ◽  
Author(s):  
Daniel Duverney ◽  
Keiji Nishioka ◽  
Kumiko Nishioka ◽  
Iekata Shiokawa
Keyword(s):  
Continued Fraction ◽  
Fibonacci Numbers ◽  
Reciprocal Sums
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