Representations of integers as sums of four polygonal numbers and partial theta functions
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2021
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| _version_ | 1866915876667654144 |
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| author | Bringmann, Kathrin Jang, Min-Joo Kane, Ben Tse, Cheuk Hin Alvin |
| author_facet | Bringmann, Kathrin Jang, Min-Joo Kane, Ben Tse, Cheuk Hin Alvin |
| contents | 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). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2103_09653 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Representations of integers as sums of four polygonal numbers and partial theta functions Bringmann, Kathrin Jang, Min-Joo Kane, Ben Tse, Cheuk Hin Alvin Number Theory 11F11, 11F37, 11E45 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). |
| title | Representations of integers as sums of four polygonal numbers and partial theta functions |
| topic | Number Theory 11F11, 11F37, 11E45 |
| url | https://arxiv.org/abs/2103.09653 |