A Salem number of degree 6 has a minimal polynomial of the following form:
where a,b and c are integers. The trace of is
, where the sum is over the six conjugates
of , i.e., the six roots of (2.1). Two of these conjugates are and
and the remaining conjugates satisfy , so a bound on |a| implies
a bound on and hence on |b| and |c|. So, for fixed a, there is a finite
set of with . Observe that
so for all Salem numbers of degree 6. In fact, there are no
such numbers with trace -1, 4 with trace 0, 15 with trace 1, and 39 with
trace 2.