Hexagon

Submitted works

math.CA — Classical Analysis and ODEs

Arithmetic progressions with prescribed lp gaps

Contributed by Vjekoslav Kovač

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.

Primarily AI-generated textHuman understanding: some partsEuclidean Ramsey theorydensity theoremmultilinear estimateoscillatory integralsingular integral

Oct 10, 2026PDF ↗View work →

hexagon:2610.00176v1

math.CA — Classical Analysis and ODEs

Superexponentially decaying sequences in the Erdos similarity problem

Contributed by Vjekoslav Kovač

We prove a non-universality criterion for the Erd\H{o}s similarity conjecture that applies beyond exponential (i.e., geometric) decay. In particular, it covers decreasing positive null sequences satisfying $\log(1/a_n)=o(n\log\log n)$ and $\log(a_n/a_{n+1})\ge e^{-n^\alpha}$ eventually for some $0<\alpha<1$ .

Primarily AI-generated textHuman understanding: some partsLebesgue measureconfigurationmeasure theory

Oct 10, 2026PDF ↗View work →