A finiteness theorem for universal $m$-gonal forms

TL;DR

This paper investigates the conditions under which certain $m$-gonal forms can represent all positive integers, establishing a finiteness theorem that characterizes their universality.

Contribution

It introduces a finiteness theorem for universal $m$-gonal forms, providing a key criterion for their universality.

Findings

Proves a finiteness theorem for universal $m$-gonal forms

Characterizes the set of positive integers related to universality

Provides criteria to determine universality of $m$-gonal forms

Abstract

In this paper, we study the set of positive integers that characterize the universality of $m$-gonal form.