  By the m-spectrum of a real number q>1 we mean the set Y^m(q) of values p(q)
where p runs over the height m polynomials with integer coefficients. These
sets have been extensively investigated during the last fifty years because of
their intimate connections with infinite Bernoulli convolutions, spectral
properties of substitutive point sets and expansions in noninteger bases. We
prove that Y^m(q) has an accumulation point if and only if q<m+1 and q is not a
Pisot number. Consequently a number of related results on the distribution of
points of this form are improved.
