Result: Complexities of finite families of polynomials, Weyl systems, and constructions in combinatorial number theory
Title:
Complexities of finite families of polynomials, Weyl systems, and constructions in combinatorial number theory
Authors:
Contributors:
Department of mathematics, OSU, The Ohio State University [Columbus] (OSU), Laboratoire de Mathématiques et Physique Théorique (LMPT), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS)
Source:
Journal d'analyse mathématique. 103:47-92
Publisher Information:
HAL CCSD; Springer, 2007.
Publication Year:
2007
Collection:
collection:UNIV-TOURS
collection:CNRS
collection:LMPT
collection:TDS-MACS
collection:IDP
collection:TEST3-HALCNRS
collection:CNRS
collection:LMPT
collection:TDS-MACS
collection:IDP
collection:TEST3-HALCNRS
Subject Terms:
Original Identifier:
HAL: hal-00017730
Document Type:
Journal
article<br />Journal articles
Language:
English
ISSN:
0021-7670
1565-8538
1565-8538
Access URL:
Rights:
info:eu-repo/semantics/OpenAccess
Accession Number:
edshal.hal.00017730v2
Database:
HAL
Further Information
We introduce two notions of complexity of a system of polynomials $p_{1},\ld,p_{r}\in\Z[n]$ and apply them to characterize the limits of the expressions of the form $\mu(A_{0}\cap T^{-p_{1}(n)}A_{1}\cap\ld\cap T^{-p_{r}(n)}A_{r})$ where $T$ is a skew-product transformation of a torus $\T^{d}$ and $A_{i}\sle\T^{d}$ are measurable sets. The obtained dynamical results allow us to construct subsets of integers with specific combinatorial properties related to the polynomial Szemer\'{e}di theorem.