Sums of generalized polygonal numbers of almost prime "length"
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929507512877056 |
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| author | Banerjee, Soumyarup Kane, Ben Kim, Daejun |
| author_facet | Banerjee, Soumyarup Kane, Ben Kim, Daejun |
| contents | In this paper, we consider sums of three generalized $m$-gonal numbers whose parameters are restricted to integers with a bounded number of prime divisors. With some restrictions on $m$ modulo $30$, we show that a density one set of integers is represented as such a sum, where the parameters are restricted to have at most 6361 prime factors. Moreover, if the squarefree part of $f_m(n)$ is sufficiently large, then $n$ is represented as such a sum, where $f_m(n)$ is a natural linear function in $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_07895 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sums of generalized polygonal numbers of almost prime "length" Banerjee, Soumyarup Kane, Ben Kim, Daejun Number Theory 11F27, 11F37, 11E20, 11E45, 11N36 In this paper, we consider sums of three generalized $m$-gonal numbers whose parameters are restricted to integers with a bounded number of prime divisors. With some restrictions on $m$ modulo $30$, we show that a density one set of integers is represented as such a sum, where the parameters are restricted to have at most 6361 prime factors. Moreover, if the squarefree part of $f_m(n)$ is sufficiently large, then $n$ is represented as such a sum, where $f_m(n)$ is a natural linear function in $n$. |
| title | Sums of generalized polygonal numbers of almost prime "length" |
| topic | Number Theory 11F27, 11F37, 11E20, 11E45, 11N36 |
| url | https://arxiv.org/abs/2409.07895 |