On the Iwasawa invariants of certain real Abelian fields

For any totally real number field k and any prime number p, the Iwasawa lambda-invariant and the mu-invariant are conjectured to be both zero. We give a new efficient method to verify this conjecture for certain real abelian fields. The new features of our method compared with other existing ones are that we use effectively cyclotomic units and that we introduce a new way to apply p-adic L-functions to the conjecture.