 

Toufik Zaïmi
On εPisot numbers


Published: 
August 26, 2009

Keywords: 
Special algebraic integers, Number fields 
Subject: 
11R06, 11R04, 12D10 


Abstract
An algebraic integer whose other conjugates over the field of the
rationals Q are of modulus less than ε,
where 0<ε ≦ 1, is called an
εPisot number. A Salem number is a real algebraic integer
greater than 1 all of whose other conjugates over Q
belong to the closed unit disc, with at least one of them of
modulus 1. Let K be a number field generated over Q
by a Salem number. We prove that there is a finite subset, say
F_{ε}, of the integers of K
such that each Salem number generating K over Q
can be written as a sum of an element of F_{ε }
and an εPisot number. We also show some
analytic properties of the set of εPisot numbers.


Author information
Département de Mathématiques, Université Larbi Ben M'hidi, Oum El Bouaghi 04000, Algérie
toufikzaimi@yahoo.com

