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p-adic Equiangular Lines and p-adic van Lint-Seidel Relative Bound
Version 1
: Received: 18 July 2024 / Approved: 18 July 2024 / Online: 19 July 2024 (09:33:39 CEST)
How to cite: KRISHNA, K. M. p-adic Equiangular Lines and p-adic van Lint-Seidel Relative Bound. Preprints 2024, 2024071562. https://doi.org/10.20944/preprints202407.1562.v1 KRISHNA, K. M. p-adic Equiangular Lines and p-adic van Lint-Seidel Relative Bound. Preprints 2024, 2024071562. https://doi.org/10.20944/preprints202407.1562.v1
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 |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
Keywords
Equiangular lines, p-adic Hilbert space.
Subject
Computer Science and Mathematics, Analysis
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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