Multiplicative dependence of shifted algebraic numbers

• Autorzy: Paulius Drungilas , Artūras Dubickas
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11R04: Algebraic numbers; rings of algebraic integers
• 11D72: Equations in many variables
• 11D57: Multiplicative and norm form equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2003
• Tom: 96
• Numer: 1
• Strony: 75-81

Daty

wydano

2003

Twórcy

autor

Paulius Drungilas

• Department of Mathematics and Informatics, Vilnius University, Naugarduko 24, Vilnius 2600, Lithuania

autor

Artūras Dubickas

• Department of Mathematics and Informatics, Vilnius University, Naugarduko 24, Vilnius 2600, Lithuania

Identyfikatory

DOI

10.4064/cm96-1-7