A Structure Theorem for Level Sets of Multiplicative Functions and Applications
2020
Abstract
Given a level set E of an arbitrary multiplicative function f, we establish, by building on the fundamental work of Frantzikinakis and Host [14, 15], a structure theorem that gives a decomposition of $1_{E}$ into an almost periodic and a pseudo-random part. Using this structure theorem together with the technique developed by the authors in [3], we obtain the following result pertaining to polynomial multiple recurrence.
Details
Title
A Structure Theorem for Level Sets of Multiplicative Functions and Applications
Published in
International Mathematics Research Notices
Volume
2020
Issue
5
Pages
1300-1345
Date
2020-03-01
ISSN
1073-7928
Other identifier(s)
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Laboratories
ERG
Record Appears in
Scientific production and competences > SB - School of Basic Sciences > MATH - Institute of Mathematics > ERG - Chair of Ergodic Theory
Peer-reviewed publications
Work outside EPFL
Journal Articles
Published
Peer-reviewed publications
Work outside EPFL
Journal Articles
Published
Record creation date
2021-11-26