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arXiv · 2408.00810

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.

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BibTeXRIS

K. Mahesh Krishna. 2024-08-01. p-adic Equiangular Lines and p-adic van Lint-Seidel Relative Bound. https://doi.org/10.4064/ba240825-18-10

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