On determinants involving $(\frac{j^2-k^2}p)$ and $(\frac{jk}p)$
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912002286288896 |
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| author | Chen, Deyi Sun, Zhi-Wei |
| author_facet | Chen, Deyi Sun, Zhi-Wei |
| contents | Let $p$ be an odd prime and let $(\frac{\cdot}p)$ be the Legendre symbol. In this paper, we study the determinant $$\det\left[\left(\frac{j^2-k^2}p\right)+\left(\frac{jk}p\right)w\right]_{δ\le j,k\le (p-1)/2}$$ with $δ\in\{0,1\}$. For example, we prove that the determinant does not depend on $w$ if $p\equiv3\pmod4$ and $δ=0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_14401 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On determinants involving $(\frac{j^2-k^2}p)$ and $(\frac{jk}p)$ Chen, Deyi Sun, Zhi-Wei Number Theory 11A15, 11C20, 15A15 Let $p$ be an odd prime and let $(\frac{\cdot}p)$ be the Legendre symbol. In this paper, we study the determinant $$\det\left[\left(\frac{j^2-k^2}p\right)+\left(\frac{jk}p\right)w\right]_{δ\le j,k\le (p-1)/2}$$ with $δ\in\{0,1\}$. For example, we prove that the determinant does not depend on $w$ if $p\equiv3\pmod4$ and $δ=0$. |
| title | On determinants involving $(\frac{j^2-k^2}p)$ and $(\frac{jk}p)$ |
| topic | Number Theory 11A15, 11C20, 15A15 |
| url | https://arxiv.org/abs/2408.14401 |