@article{HajimeKaneko2015,
abstract = {Let d ≥ 2 be an integer. In 2010, the second, third, and fourth authors gave necessary and sufficient conditions for the infinite products
$∏_\{k=1 \atop U_\{d^k\}≠-a_i\}^\{∞\} (1 + (a_i)/(U_\{d^k\}))$ (i=1,...,m) or $∏_\{k=1 \atop V_\{d^k\}≠-a_i\}^\{∞\} (1 + (a_i)(V_\{d^k\})$ (i=1,...,m)
to be algebraically dependent, where $a_i$ are non-zero integers and $U_n$ and $V_n$ are generalized Fibonacci numbers and Lucas numbers, respectively. The purpose of this paper is to relax the condition on the non-zero integers $a_1,...,a_m$ to non-zero real algebraic numbers, which gives new cases where the infinite products above are algebraically dependent.},
author = {Hajime Kaneko, Takeshi Kurosawa, Yohei Tachiya, Taka-aki Tanaka},
journal = {Acta Arithmetica},
keywords = {algebraic dependence; infinite products; Fibonacci numbers; Lucas numbers; Mahler's method},
language = {eng},
number = {2},
pages = {161-186},
title = {Explicit algebraic dependence formulae for infinite products related with Fibonacci and Lucas numbers},
url = {http://eudml.org/doc/279621},
volume = {168},
year = {2015},
}
TY - JOUR
AU - Hajime Kaneko
AU - Takeshi Kurosawa
AU - Yohei Tachiya
AU - Taka-aki Tanaka
TI - Explicit algebraic dependence formulae for infinite products related with Fibonacci and Lucas numbers
JO - Acta Arithmetica
PY - 2015
VL - 168
IS - 2
SP - 161
EP - 186
AB - Let d ≥ 2 be an integer. In 2010, the second, third, and fourth authors gave necessary and sufficient conditions for the infinite products
$∏_{k=1 \atop U_{d^k}≠-a_i}^{∞} (1 + (a_i)/(U_{d^k}))$ (i=1,...,m) or $∏_{k=1 \atop V_{d^k}≠-a_i}^{∞} (1 + (a_i)(V_{d^k})$ (i=1,...,m)
to be algebraically dependent, where $a_i$ are non-zero integers and $U_n$ and $V_n$ are generalized Fibonacci numbers and Lucas numbers, respectively. The purpose of this paper is to relax the condition on the non-zero integers $a_1,...,a_m$ to non-zero real algebraic numbers, which gives new cases where the infinite products above are algebraically dependent.
LA - eng
KW - algebraic dependence; infinite products; Fibonacci numbers; Lucas numbers; Mahler's method
UR - http://eudml.org/doc/279621
ER -
