Computation of the Iwasawa invariants of certain real abelian fields

Let p be a prime number and k a finite extension of Q. It is conjectured that the Iwasawa invariants lambda(p)(k) and mu(p) (k) vanish for all p and totally real number fields k. Some methods to verify the conjecture for each real abelian field k are known, in which cyclotomic units and a set of auxiliary prime numbers are used. We give an effective method, based on the previous one, to compute the exact value of the other Iwasawa invariant v,(k) by using Gauss sums and another set of auxiliary prime numbers. As numerical examples, we compute the Iwasawa invariants associated to k = Q(rootf, xi(p) + xi(p)(-1)) in the range 1<f < 200 and 5less than or equal top <10000. (C) 2003 Elsevier Inc. All rights reserved.