An analogue of a formula of Popov
Fuente:
arXiv
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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866913466541932544 |
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| author | Ribeiro, Pedro |
| author_facet | Ribeiro, Pedro |
| contents | Let $r_{k}(n)$ denote the number of representations of the positive integer $n$ as the sum of $k$ squares. We prove a new summation formula involving $r_{k}(n)$ and the Bessel functions of the first kind, which constitutes an analogue of a result due to the Russian mathematician A. I. Popov. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_01759 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An analogue of a formula of Popov Ribeiro, Pedro Number Theory Classical Analysis and ODEs Let $r_{k}(n)$ denote the number of representations of the positive integer $n$ as the sum of $k$ squares. We prove a new summation formula involving $r_{k}(n)$ and the Bessel functions of the first kind, which constitutes an analogue of a result due to the Russian mathematician A. I. Popov. |
| title | An analogue of a formula of Popov |
| topic | Number Theory Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2408.01759 |