Regular $m$-gonal forms

TL;DR

This paper proves finiteness results for regular m-gonal forms of fixed rank and classifies all such forms for large m, advancing understanding in number theory and polygonal forms.

Contribution

It establishes finiteness of m values for regular m-gonal forms of fixed rank and classifies all such forms for sufficiently large m.

Findings

Finiteness of m for regular m-gonal forms of fixed rank n.

Complete classification of regular m-gonal forms for large m.

Identification of all types of these forms.

Abstract

In this paper, we show that for a fixed rank $n$, there are only finitely many $m$ for which there is a regular $m$-gonal form of rank $n$ and determine every type of the (generalized) regular $m$-gonal form for every sufficiently large $m$.