Representations of almost regular m-gonal forms II

TL;DR

This paper investigates the representation of large integers by almost regular m-gonal forms of rank at least 5, expanding understanding of their representational properties.

Contribution

It provides a detailed study of the integers represented by almost regular m-gonal forms of rank ≥ 5, focusing on large integers.

Findings

Almost regular m-gonal forms of rank ≥ 5 represent all sufficiently large locally represented integers.

The paper extends known results about regularity to almost regular forms.

It characterizes the large integers represented by these forms.

Abstract

It is known that any $m$-gonal form of rank $n \ge 5$ is almost regular. On the other words, any $m$-gonal form of rank $n \ge 5$ represents every sufficiently large integer which is locally represented. In this article, we study the sufficiently large integers which are represented by (almost regular) $m$-gonal forms of rank $n \ge 5$.