## On the Iwasawa λ-invariant of the Real $p$-cyclotomic Field

J. Math. Sci. Univ. Tokyo
Vol. 3 (1996), No. 2, Page 457--470.

Ichimura, Humio ; Sumida, Hiroki
On the Iwasawa λ-invariant of the Real $p$-cyclotomic Field
For any totally real number field $k$ and any prime number $p$, it is conjectured that the Iwasawa invariants $λ_p(k)$ and $μ_p(k)$ are both zero. We give a new criterion for the conjecture to be true when $k$ is the real $p$-cyclotomic field, introducing a new way to apply $p$-adic $L$-functions. In a sense, it is a natural "generalization" of the classical criterion for the Vandiver conjecture.