A classification of regular diagonal quadratic forms

TL;DR

This paper classifies all regular diagonal quadratic forms of rank greater than 3, expanding understanding of their structure and representation properties in number theory.

Contribution

It provides a complete classification of regular diagonal quadratic forms of rank greater than 3, a previously unresolved problem.

Findings

Complete classification of regular diagonal quadratic forms of rank > 3

Identification of all such forms that are locally but not globally represented

Enhanced understanding of the structure of regular quadratic forms

Abstract

A positive-definite integral quadratic form is called regular if it represents every positive integer which is locally represented. In this article, we classify all regular diagonal quadratic forms of rank greater than 3.