Representations of almost regular m-gonal forms I

TL;DR

This paper investigates the representation of large integers by almost regular m-gonal forms of rank at least 6, expanding understanding of their representational capabilities.

Contribution

It extends the study of m-gonal forms to rank 6 and above, focusing on the representation of sufficiently large integers by these forms.

Findings

Large integers are represented by almost regular m-gonal forms of rank ≥ 6.

The paper provides conditions under which these forms represent all sufficiently large integers.

It advances the theory of polygonal forms in number theory.

Abstract

It is known that any $m$-gonal form of $\rank n \ge 5$ is almost regular. In this article, we study the sufficiently large integers which are represented by (almost regular) $m$-gonal forms of $\rank n \ge 6$.