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 λp(k) and μp(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 νp(k) by using Gauss sums and another set of auxiliary prime numbers. As numerical examples, we compute the Iwasawa invariants associated to in the range 1