Geodesic
Multiplicative dependence of shifted algebraic numbers
Paulius Drungilas 1   ; Artūras Dubickas 1
1 Department of Mathematics and Informatics Vilnius University Naugarduko 24 Vilnius 2600, Lithuania
Colloquium Mathematicum, Tome 96 (2003) no. 1, pp. 75-81 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

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.
DOI : 10.4064/cm96-1-7
Keywords: set obtained adding sufficiently large integers fixed quadratic algebraic number multiplicatively dependent set obtained adding rational numbers fixed cubic algebraic number similar questions algebraic numbers higher degrees raised these related prouhet tarry escott type problems applied zero distribution universality zeta functions

Paulius Drungilas  1   ; Artūras Dubickas  1

1 Department of Mathematics and Informatics Vilnius University Naugarduko 24 Vilnius 2600, Lithuania 
@article{10_4064_cm96_1_7,
     author = {Paulius Drungilas and Art\={u}ras Dubickas},
     title = {Multiplicative dependence of
  shifted algebraic numbers},
     journal = {Colloquium Mathematicum},
     pages = {75--81},
     year = {2003},
     volume = {96},
     number = {1},
     doi = {10.4064/cm96-1-7},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/cm96-1-7/}
}
TY  - JOUR
AU  - Paulius Drungilas
AU  - Artūras Dubickas
TI  - Multiplicative dependence of
  shifted algebraic numbers
JO  - Colloquium Mathematicum
PY  - 2003
SP  - 75
EP  - 81
VL  - 96
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4064/cm96-1-7/
DO  - 10.4064/cm96-1-7
LA  - en
ID  - 10_4064_cm96_1_7
ER  - 
%0 Journal Article
%A Paulius Drungilas
%A Artūras Dubickas
%T Multiplicative dependence of
  shifted algebraic numbers
%J Colloquium Mathematicum
%D 2003
%P 75-81
%V 96
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4064/cm96-1-7/
%R 10.4064/cm96-1-7
%G en
%F 10_4064_cm96_1_7
Paulius Drungilas; Artūras Dubickas. Multiplicative dependence of
  shifted algebraic numbers. Colloquium Mathematicum, Tome 96 (2003) no. 1, pp. 75-81. doi: 10.4064/cm96-1-7

Cité par Sources :