An Equidistribution Result for Differences Associated with Square Pyramidal Numbers
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913800684306432 |
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| author | Dong, Anji Saettone, Katerina Song, Kendra Zaharescu, Alexandru |
| author_facet | Dong, Anji Saettone, Katerina Song, Kendra Zaharescu, Alexandru |
| contents | We provide an asymptotic formula for the average value of the sequence A351830: $a_{n} = |P_{n} - y^{2}_{n}|$ for $1 \leq n \leq x$, where $P_{n}$ is the $n$-th square pyramidal number and $y^{2}_{n}$ is the closest square to $P_{n}$. Moreover, we supply asymptotic formulas for the $k$-th moment of the same sequence, for any fixed natural number $k$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_10097 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An Equidistribution Result for Differences Associated with Square Pyramidal Numbers Dong, Anji Saettone, Katerina Song, Kendra Zaharescu, Alexandru Number Theory 11L07, 11B99, 11K38, 11K06 We provide an asymptotic formula for the average value of the sequence A351830: $a_{n} = |P_{n} - y^{2}_{n}|$ for $1 \leq n \leq x$, where $P_{n}$ is the $n$-th square pyramidal number and $y^{2}_{n}$ is the closest square to $P_{n}$. Moreover, we supply asymptotic formulas for the $k$-th moment of the same sequence, for any fixed natural number $k$. |
| title | An Equidistribution Result for Differences Associated with Square Pyramidal Numbers |
| topic | Number Theory 11L07, 11B99, 11K38, 11K06 |
| url | https://arxiv.org/abs/2412.10097 |