{"title":"p-adic Equiangular Lines and p-adic van Lint-Seidel Relative Bound","authors":"K. Mahesh Krishna","doi":"arxiv-2408.00810","DOIUrl":null,"url":null,"abstract":"We introduce the notion of p-adic equiangular lines and derive the first\nfundamental relation between common angle, dimension of the space and the\nnumber of lines. More precisely, we show that if $\\{\\tau_j\\}_{j=1}^n$ is p-adic\n$\\gamma$-equiangular lines in $\\mathbb{Q}^d_p$, then \\begin{align*} (1)\n\\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\nbelieve that this complements fundamental van Lint-Seidel \\textit{[Indag.\nMath., 1966]} relative bound for equiangular lines in the p-adic case.","PeriodicalId":501373,"journal":{"name":"arXiv - MATH - Spectral Theory","volume":"34 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Spectral Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.00810","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
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.