Algebraic Independence of Infinite Products and Their Derivatives

2013 ◽  
pp. 143-156 ◽  
Author(s):  
Peter Bundschuh
Keyword(s):  
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 properties related to certain infinite products

2011 ◽  
Author(s):  
Taka-aki Tanaka ◽  
Masaaki Amou ◽  
Masanori Katsurada
Keyword(s):  
Algebraic Independence ◽  
Infinite Products ◽  
Independence Properties

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.

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 On algebraic independence of a class of infinite products

2017 ◽  
Vol 172 ◽  
pp. 114-132 ◽  
Author(s):  
Masaaki Amou ◽  
Keijo Väänänen
Keyword(s):  
Algebraic Independence ◽  
Infinite Products

Productly linearly independent sequences

2015 ◽  
Vol 52 (3) ◽  
pp. 350-370
Author(s):  
Jaroslav Hančl ◽  
Katarína Korčeková ◽  
Lukáš Novotný
Keyword(s):  
Rational Numbers ◽  
Infinite Products ◽  
Linearly Independent ◽  
New Concepts ◽  
Infinite Sequences

We introduce the two new concepts, productly linearly independent sequences and productly irrational sequences. Then we prove a criterion for which certain infinite sequences of rational numbers are productly linearly independent. As a consequence we obtain a criterion for the irrationality of infinite products and a criterion for a sequence to be productly irrational.

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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