Non-almost regular quaternary $m$-gonal forms

TL;DR

This paper investigates the properties of non-almost regular quaternary m-gonal forms, focusing on those of rank 4, and establishes that the maximum such rank is 4.

Contribution

It characterizes the non-almost regular m-gonal forms of rank 4, identifying the maximal rank for such forms as 4.

Findings

The maximal rank for non-almost regular m-gonal forms is 4.

The paper classifies non-almost regular m-gonal forms of rank 4.

Abstract

The maximal $n$ which admits a non-almost regular $m$-gonal form of rank $n$ is $4$. In this article, we consider the $m$-gonal forms of rank $4$ which is not almost regular.