p-adic Equiangular Lines and p-adic van Lint-Seidel Relative Bound
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913957462147072 |
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| author | Krishna, K. Mahesh |
| author_facet | Krishna, K. Mahesh |
| contents | We introduce the notion of p-adic equiangular lines and derive the first fundamental relation between common angle, dimension of the space and the number of lines. More precisely, we show that if $\{τ_j\}_{j=1}^n$ is p-adic $γ$-equiangular lines in $\mathbb{Q}^d_p$, then \begin{align*} (1) \quad\quad \quad \quad |n|^2\leq |d|\max\{|n|, γ^2 \}. \end{align*} We call Inequality (1) as the p-adic van Lint-Seidel relative bound. We believe that this complements fundamental van Lint-Seidel \textit{[Indag. Math., 1966]} relative bound for equiangular lines in the p-adic case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_00810 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | p-adic Equiangular Lines and p-adic van Lint-Seidel Relative Bound Krishna, K. Mahesh Combinatorics Functional Analysis Number Theory Spectral Theory 12J25, 46S10, 47S10, 11D88 We introduce the notion of p-adic equiangular lines and derive the first fundamental relation between common angle, dimension of the space and the number of lines. More precisely, we show that if $\{τ_j\}_{j=1}^n$ is p-adic $γ$-equiangular lines in $\mathbb{Q}^d_p$, then \begin{align*} (1) \quad\quad \quad \quad |n|^2\leq |d|\max\{|n|, γ^2 \}. \end{align*} We call Inequality (1) as the p-adic van Lint-Seidel relative bound. We believe that this complements fundamental van Lint-Seidel \textit{[Indag. Math., 1966]} relative bound for equiangular lines in the p-adic case. |
| title | p-adic Equiangular Lines and p-adic van Lint-Seidel Relative Bound |
| topic | Combinatorics Functional Analysis Number Theory Spectral Theory 12J25, 46S10, 47S10, 11D88 |
| url | https://arxiv.org/abs/2408.00810 |