{"id":"hexagon/2610.00185","pdf":"https://hexagonmath.org/pdf/2610.00185v1","url":"https://hexagonmath.org/abs/2610.00185v1","tags":["math.CO","msc:42B20","msc:05D10","msc:11B30","Euclidean Ramsey theory","density theorem","multilinear estimate","oscillatory integral","singular integral"],"score":0,"title":"Arithmetic progressions with prescribed lp gaps","domain":"math.CA","origin":"ai-generated","source":"hexagon","authors":["Vjekoslav Kovač"],"reviews":0,"subject":"math.CA","summary":"For every $n\\ge3$ and $p\\in[1,\\infty)\\setminus\\{1,2,\\ldots,n-1\\}$, we prove that every measurable subset of $\\mathbf{R}^d$ of positive upper Banach density, with $d\\ge2^{n-2}+1$, contains an $n$-term arithmetic progression with every sufficiently large prescribed $\\ell^p$ gap.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["ChatGPT","ChatGPT"],"discussed":0,"published":"2026-10-10","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}