Representations of integers as sums of four polygonal numbers and partial theta functions
Number Theory
2026-03-23 v2
Abstract
In this paper, we consider representations of integers as sums of at most four distinct -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 -gon) is asymptotically the same as times the number of such representations with arbitrary integer parameters (often called generalized polygonal numbers).
Keywords
Cite
@article{arxiv.2103.09653,
title = {Representations of integers as sums of four polygonal numbers and partial theta functions},
author = {Kathrin Bringmann and Min-Joo Jang and Ben Kane and Cheuk Hin Alvin Tse},
journal= {arXiv preprint arXiv:2103.09653},
year = {2026}
}