Class number of real quadratic fields of explicit discriminant

TL;DR

This paper investigates the class numbers of certain real quadratic fields with explicitly known continued fraction expansions of their discriminants, establishing that most have class number greater than one.

Contribution

It proves that for a family of real quadratic fields with known discriminant expansions, the class number exceeds one, with only finitely many possible exceptions.

Findings

Most fields in the family have class number greater than one.

The paper identifies conditions under which the class number exceeds one.

There may be finitely many exceptions to the class number being greater than one.

Abstract

In this paper we are interested in the class numbers of a family of real quadratic fields for which the square roots of the discriminants have a known expansion in continued fraction. In particular we prove that $h(D)>1$, with possibly a finite number of exceptions.