Multiplicative dependence of shifted algebraic numbers

Paulius Drungilas, and Artūras Dubickas. "Multiplicative dependence of shifted algebraic numbers." Colloquium Mathematicae 96.1 (2003): 75-81. <http://eudml.org/doc/285137>.

@article{PauliusDrungilas2003,
abstract = {We show that the set obtained by adding all sufficiently large integers to a fixed quadratic algebraic number is multiplicatively dependent. So also is the set obtained by adding rational numbers to a fixed cubic algebraic number. Similar questions for algebraic numbers of higher degrees are also raised. These are related to the Prouhet-Tarry-Escott type problems and can be applied to the zero-distribution and universality of some zeta-functions.},
author = {Paulius Drungilas, Artūras Dubickas},
journal = {Colloquium Mathematicae},
keywords = {algebraic numbers; Prouhet-Tarry-Escott problem; multiplicative dependence},
language = {eng},
number = {1},
pages = {75-81},
title = {Multiplicative dependence of shifted algebraic numbers},
url = {http://eudml.org/doc/285137},
volume = {96},
year = {2003},
}

TY - JOUR
AU - Paulius Drungilas
AU - Artūras Dubickas
TI - Multiplicative dependence of shifted algebraic numbers
JO - Colloquium Mathematicae
PY - 2003
VL - 96
IS - 1
SP - 75
EP - 81
AB - We show that the set obtained by adding all sufficiently large integers to a fixed quadratic algebraic number is multiplicatively dependent. So also is the set obtained by adding rational numbers to a fixed cubic algebraic number. Similar questions for algebraic numbers of higher degrees are also raised. These are related to the Prouhet-Tarry-Escott type problems and can be applied to the zero-distribution and universality of some zeta-functions.
LA - eng
KW - algebraic numbers; Prouhet-Tarry-Escott problem; multiplicative dependence
UR - http://eudml.org/doc/285137
ER -