On the cyclotomic field $\mathbb{Q}(e^{2π{\bf i}/p})$ and Zhi-Wei Sun's conjecture on $\det M_p$
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912253899440128 |
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| author | Wang, Li-Yuan Wu, Hai-Liang |
| author_facet | Wang, Li-Yuan Wu, Hai-Liang |
| contents | In 2019, Zhi-Wei Sun posed an interesting conjecture on certain determinants with Legendre symbol entries. In this paper, by using the arithmetic properties of $p$-th cyclotomic field and the finite field $\mathbb{F}_p$, we confirm this conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_05853 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the cyclotomic field $\mathbb{Q}(e^{2π{\bf i}/p})$ and Zhi-Wei Sun's conjecture on $\det M_p$ Wang, Li-Yuan Wu, Hai-Liang Number Theory In 2019, Zhi-Wei Sun posed an interesting conjecture on certain determinants with Legendre symbol entries. In this paper, by using the arithmetic properties of $p$-th cyclotomic field and the finite field $\mathbb{F}_p$, we confirm this conjecture. |
| title | On the cyclotomic field $\mathbb{Q}(e^{2π{\bf i}/p})$ and Zhi-Wei Sun's conjecture on $\det M_p$ |
| topic | Number Theory |
| url | https://arxiv.org/abs/2401.05853 |