p-adic Equiangular Lines and p-adic van Lint-Seidel Relative Bound

K. Mahesh Krishna
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Abstract

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 $\{\tau_j\}_{j=1}^n$ is p-adic $\gamma$-equiangular lines in $\mathbb{Q}^d_p$, then \begin{align*} (1) \quad\quad \quad \quad |n|^2\leq |d|\max\{|n|, \gamma^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.
p-adic 等边线和 p-adic van Lint-Seidel 相对边界
我们引入了 p-adic 等角线的概念,并推导出公角、空间维数和线数之间的第一个基本关系。更准确地说,我们证明了如果 $\{tau_j\}_{j=1}^n$ 是 $\mathbb{Q}^d_p$ 中的 p-adic$\gamma$ 等角线,那么 \begin{align*} (1)\quad\quad \quad |n|^2\leq |d|\max\{|n|, \gamma^2 \}。\end{align*}我们把不等式 (1) 称为 p-adic van Lint-Seidel 相对约束。我们认为这是对 p-adic 情况下等边线的基本 van Lint-Seidel (textit{[Indag.Math.,1966]})相对约束的补充。
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