On ε-Pisot numbers
Toufik Za ̈ imi · 2009
An algebraic integer whose other conjugates over the field of the rationals Q are of modulus less than e ,w here 0 <e ≤ 1, is called an e-Pisot 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 Fe, of the integers of K such that each Salem number generating K over Q can be written as as um of an element ofFe and an e-Pisot number. We also show some analytic properties of the set of e-Pisot numbers.