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arXiv · 2103.09653

Representations of integers as sums of four polygonal numbers and partial theta functions

Kathrin Bringmann·Min-Joo Jang·Ben Kane·Cheuk Hin Alvin Tse
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Abstract

In this paper, we consider representations of integers as sums of at most four distinct $m$-gonal numbers (allowing a fixed number of repeats of each polygonal number occurring in the sum). We show that the number of such representations with non-negative parameters (hence counting the number of points in a regular $m$-gon) is asymptotically the same as $\frac{1}{16}$ times the number of such representations with arbitrary integer parameters (often called generalized polygonal numbers).

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Kathrin Bringmann, Min-Joo Jang, Ben Kane, Cheuk Hin Alvin Tse. 2021-03-17. Representations of integers as sums of four polygonal numbers and partial theta functions. https://arxiv.org/abs/2103.09653

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