Construction of image with prescribed Iwasawa λ-invariants Original Research Article

It is a basic problem in Iwasawa theory that the existence of a image-extension with prescribed Iwasawa invariants. Since the Iwasawa λ-invariant is regarded as an analogue of (twice of) the genus of an algebraic curve, we are especially interested in the problem on the Iwasawa λ-invariants. In this article, for a few prime numbers p, we show that there is a image-extension with prescribed Iwasawa λ-invariant by using Kidaʹs formula, which is a number field analogue of the Riemann–Hurwitz formula.