On the Distances Between Pisot Numbers Generating the Same Number Field

LetKbe a real algebraic number field. A well-known result, due to Meyer, statesthat the set & wp;Kof Pisot numbers generatingKis uniformly discrete and relativelydense in the interval[1,infinity).A recent theorem of Dubickas yields that an algebraicinteger, generatingK,belongs to the set & wp;K - & wp;Kif and only if its other conjugatesare of modulus less than 2.In the present paper, we show that 1 is an element of & wp;K-& wp;K,andifKis totally real, then the elements of & wp;K-& wp;Kare all algebraic integers ofKwhose images under the action of all embeddings ofKintoR,other than the identityofK,belong to the interval(-2,2).Also, we prove that set{theta '-theta|theta 'is an element of & wp;K,theta is an element of & wp;K,theta '>theta and(theta, theta ')boolean AND & wp;K=& empty;}is finite and contains at least two elements(resp. at least 2deg(K)-1)elements whenKACK=Q(resp. whenKis totally real).