Multiple recurence and convergence for sequences related to the prime numbers
| dc.creator | Frantzikinakis, Nikos | |
| dc.creator | Host, Bernard | |
| dc.creator | Kra, Bryna | |
| dc.date | 2006-07-25 | |
| dc.date.accessioned | 2026-07-07T07:20:55Z | |
| dc.date.available | 2026-07-07T07:20:55Z | |
| dc.description | For any measure preserving system $(X,\mathcal{X},μ,T)$ and $A\in\mathcal{X}$ with $μ(A)>0$, we show that there exist infinitely many primes $p$ such that $μ\bigl(A\cap T^{-(p-1)}A\cap T^{-2(p-1)}A\bigr) > 0$ (the same holds with $p-1$ replaced by $p+1$). Furthermore, we show the existence of the limit in $L^2(μ)$ of the associated ergodic average over the primes. A key ingredient is a recent result of Green and Tao on the von Mangoldt function. A combinatorial consequence is that every subset of the integers with positive upper density contains an arithmetic progression of length three and common difference of the form $p-1$ (or $p+1$) for some prime $p$. | |
| dc.description | 14 pages. To appear in Crelle's Journal | |
| dc.identifier | https://arxiv.org/abs/math/0607637 | |
| dc.identifier | http://arxiv.org/abs/math/0607637 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/115120 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Combinatorics | |
| dc.subject | 37A30, 28D05 | |
| dc.title | Multiple recurence and convergence for sequences related to the prime numbers | |
| dc.type | text |