On ε-Pisot numbers

摘要

An algebraic integer whose other conjugates over the field of therationals Q are of modulus less than ε,where 0ε ≦ 1, is called an ε-Pisot number. A Salem number is a real algebraic integergreater than 1 all of whose other conjugates over Qbelong to the closed unit disc, with at least one of them ofmodulus 1. Let K be a number field generated over Q by a Salem number. We prove that there is a finite subset, say Fε, of the integers of Ksuch that each Salem number generating K over Q can be written as a sum of an element of Fε and an ε-Pisot number. We also show someanalytic properties of the set of ε-Pisot numbers.