On the plus parts of the class numbers of cyclotomic fields

TL;DR

This paper introduces new families of cyclotomic fields with non-trivial plus parts of their class numbers and proves 3-divisibility for infinitely many such fields, supported by numerical examples.

Contribution

It presents new families of cyclotomic fields with specific class number properties and establishes 3-divisibility results for their plus parts.

Findings

New families of cyclotomic fields with non-trivial plus class numbers

Proof of 3-divisibility of plus class numbers in infinitely many cases

Numerical examples supporting theoretical results

Abstract

We exhibit some new families of cyclotomic fields which have non-trivial plus parts of their class numbers. We also prove the $3$ - divisibility of the plus part of the class number of another family consisting of infinitely many cyclotomic fields. At the end, we provide some numerical examples supporting our results.