On the vanishing of Iwasawa's constant $\mu$ for the cyclotomic $\Z_p$-extensions of $CM$ number fields

TL;DR

This paper proves that Iwasawa's mu-invariant vanishes for cyclotomic old extensions of CM number fields, confirming a key conjecture in Iwasawa theory for these fields.

Contribution

It establishes the vanishing of or the cyclotomic old extensions of CM number fields, advancing understanding in Iwasawa theory.

Findings

ollows from the proof that or these extensions.

Supports the main conjecture in Iwasawa theory for CM fields.

Provides a key step towards understanding class group growth in cyclotomic extensions.

Abstract

We prove that $\mu = 0$ for the cyclotomic $\Z_p$-extensions of CM number fields.