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

scholarly journals Algebraic independence properties of the Fredholm series

1978 ◽  
Vol 26 (1) ◽  
pp. 31-45 ◽  
Author(s):  
J. H. Loxton ◽  
A. J. van der Poorten
Keyword(s):  
Algebraic Independence ◽  
Rational Functions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Algebraic Numbers ◽  
Independence Properties ◽  
Image Position ◽  
Necessary And Sufficient

AbstractWe consider algebraic independence properties of series such as We show that the functions fr(z) are algebraically independent over the rational functions Further, if αrs (r = 2, 3, 4, hellip; s = 1, 2, 3, hellip) are algebraic numbers with 0 < |αrs|, we obtain an explicit necessary and sufficient condition for the algebraic independence of the numbers fr(αrs) over the rationals.

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

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
Sign in / Sign up

Export Citation Format

Share Document