  Let p be an odd prime, n an odd positive integer and C the p-Sylow subgroup
the class group of the p-cyclotomic extension of the rationals. When log(p) is
bigger than n**(224n**4), we prove that the eigenspace on C attached to the
(p-n)-th power of the Teichmuller character is trivial. The proof uses the
K-theory of the integers and the Voronoi reduction theory of quadratic forms.
