Parameterized families of quadratic fields with $n$-rank at least 2

TL;DR

This paper constructs parameterized families of quadratic fields, both imaginary and real, that have class groups with an n-rank of at least 2, advancing understanding of class group structures.

Contribution

It introduces explicit parameterized families of quadratic fields with prescribed n-rank properties, a novel approach in algebraic number theory.

Findings

Constructed infinite families of quadratic fields with n-rank ≥ 2

Demonstrated methods to control class group structures

Extended previous results on class group ranks

Abstract

We construct parameterized families of imaginary (resp. real) quadratic fields whose class groups have $n$-rank at least $2$.