Class groups of imaginary quadratic fields of $3$-rank at least $2$

TL;DR

This paper constructs an infinite family of imaginary quadratic fields with ideal class groups having a 3-rank of at least 2, advancing understanding of class group structures in number theory.

Contribution

The paper introduces a method to generate infinitely many imaginary quadratic fields with specified 3-rank properties, providing new examples and insights into class group behavior.

Findings

Infinite family of imaginary quadratic fields with 3-rank ≥ 2

Explicit construction method for such fields

Enhanced understanding of class group structures in quadratic fields

Abstract

We produce an infinite family of imaginary quadratic fields whose ideal class groups have $3$-rank at least $2$.