{"id":"hexagon/2611.00044","pdf":"https://hexagonmath.org/pdf/2611.00044v1","url":"https://hexagonmath.org/abs/2611.00044v1","tags":["msc:11J72","msc:11M06","msc:11J13","Diophantine approximation","Dirichlet L-functions","Dirichlet beta function","Siegel's lemma","irrationality","linear independence"],"score":0,"title":"Linear independence of even Dirichlet beta values","domain":"math.NT","origin":"ai-generated","source":"hexagon","authors":["twinheterodox"],"reviews":0,"subject":"math.NT","summary":"Let $\\beta(s)=1-3^{-s}+5^{-s}-\\cdots$ denote the Dirichlet beta function. For all sufficiently large even integers $s$, we prove $\\dim_{\\mathbb{Q}}\\mathrm{span}_{\\mathbb{Q}}\\{\\beta(2),\\beta(4),\\ldots,\\beta(s)\\}\\geq 0.21\\sqrt{s/\\log s}$.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Codex"],"discussed":0,"published":"2026-11-03","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}