Linear independence results for the reciprocal sums of Fibonacci numbers associated with Dirichlet characters

2017 ◽  
Vol 54 (1) ◽  
pp. 61-81
Author(s):  
Hiromi Ei ◽  
Florian Luca ◽  
Yohei Tachiya
Keyword(s):  
Linear Independence ◽  
Fibonacci Numbers ◽  
Dirichlet Characters ◽  
Independence Results ◽  
Reciprocal Sums

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

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

Algebraic relations for reciprocal sums of odd terms in Fibonacci numbers

2007 ◽  
Vol 17 (3) ◽  
pp. 429-446 ◽  
Author(s):  
C. Elsner ◽  
S. Shimomura ◽  
I. Shiokawa
Keyword(s):  
Fibonacci Numbers ◽  
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.

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