scholarly journals Algebraic independence of certain infinite products involving the Fibonacci numbers

2021 ◽  
Vol 97 (5) ◽  
Author(s):  
Daniel Duverney ◽  
Yohei Tachiya
Keyword(s):  
Fibonacci Numbers ◽  
Algebraic Independence ◽  
Infinite Products

scholarly journals Algebraic independence of infinite products generated by Fibonacci numbers

2011 ◽  
Vol 34 (2) ◽  
pp. 255-264 ◽  
Author(s):  
Takeshi Kurosawa ◽  
Yohei Tachiya ◽  
Taka-aki Tanaka
Keyword(s):  
Fibonacci Numbers ◽  
Algebraic Independence ◽  
Infinite Products

scholarly journals Hypertranscendence and algebraic independence of certain infinite products

2018 ◽  
Vol 184 (1) ◽  
pp. 51-66 ◽  
Author(s):  
Peter Bundschuh ◽  
Keijo Väänänen
Keyword(s):  
Algebraic Independence ◽  
Infinite Products

Algebraic Independence of Sums of Reciprocals of the Fibonacci Numbers

1999 ◽  
Vol 202 (1) ◽  
pp. 97-108 ◽  
Author(s):  
Kumlko Nishioka ◽  
Taka-Aki Tanaka ◽  
Takeshi Toshimitsu
Keyword(s):  
Fibonacci Numbers ◽  
Algebraic Independence

ARITHMETIC PROPERTIES OF INFINITE PRODUCTS OF CYCLOTOMIC POLYNOMIALS

2016 ◽  
Vol 93 (3) ◽  
pp. 375-387 ◽  
Author(s):  
PETER BUNDSCHUH ◽  
KEIJO VÄÄNÄNEN
Keyword(s):  
Algebraic Independence ◽  
Cyclotomic Polynomials ◽  
Infinite Products ◽  
Arithmetic Properties ◽  
Independence Results

We study transcendence properties of certain infinite products of cyclotomic polynomials. In particular, we determine all cases in which the product is hypertranscendental. We then use various results from Mahler’s transcendence method to obtain algebraic independence results on such functions and their values.

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
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