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arXiv · 2109.01597

Representation of $m$-gonal forms over $\mathbb N_0$ and a finiteness theorem for universal original version's $m$-gonal forms

Dayoon Park
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Abstract

In this article, we consider the representation of $m$-gonal forms over $\mathbb N_0$. We show that any $m$-gonal forms over $\mathbb N_0$ of rank $\ge 5$ is almost regular and ponder the sufficiently large integers which are indeed represented over $\mathbb N_0$ among the integers which are locally represented. And as its consequential result, we prove a finiteness theorem for universal (original polygonal number version's) $m$-gonal forms over $\mathbb N_0$.

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Dayoon Park. 2021-10-04. Representation of $m$-gonal forms over $\mathbb N_0$ and a finiteness theorem for universal original version's $m$-gonal forms. https://arxiv.org/abs/2109.01597

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