On certain infinite families of imaginary quadratic fields whose Iwasawa {\lambda}-invariant is equal to 1

TL;DR

This paper constructs infinite families of imaginary quadratic fields where a prime p splits and the Iwasawa λ-invariant of their cyclotomic Zp-extensions equals 1, advancing understanding of Iwasawa theory.

Contribution

It demonstrates the existence of infinite families of imaginary quadratic fields with specific splitting and Iwasawa invariants, a new result in number theory.

Findings

Existence of infinite families with λ-invariant 1

Fields where p splits in the extension

Advances in understanding Iwasawa invariants

Abstract

Let p be an odd prime number. In this paper, we show existence of certain infinite families of imaginary quadratic fields in which p splits and whose Iwasawa {\lambda}-invariant of the cyclotomic Zp-extension is equal to 1.