Iwasawa invariants and class number parity of multi-quadratic number fields

TL;DR

This paper investigates Iwasawa invariants and class number parity in multi-quadratic number fields, providing explicit formulas and criteria based on detailed analysis of units and ramification, advancing understanding in algebraic number theory.

Contribution

It offers explicit formulas for Iwasawa invariants and criteria for class number parity in multi-quadratic fields, extending previous theoretical results.

Findings

Explicit formulas for Iwasawa invariants under Greenberg's conjecture

Criteria for class number parity in multi-quadratic fields

Detailed analysis of Hasse units and ramification effects

Abstract

In this paper, based mainly on the method of Iwasawa and Kida, by studying in detail the Hasse units and the ramifications of prime ideals, we obtain explicit results of Iwasawa invariants $ \lambda_{2} $ of the cyclotomic $ \Z_{2}-$extensions of number fields. In particular, under the Greenberg's conjecture, we obtain an explicit formula of $ \lambda_{2} $ for imaginary multi-quadratic number fields. As an application, we give a criteria of determining class number parity of multi-quadratic number fields.