Geodesic
Good weights for the Erdős discrepancy problem
Discrete analysis (2020) Cet article a éte moissonné depuis la source Scholastica

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The Erdős discrepancy problem, now a theorem by T. Tao, asks whether every sequence with values plus or minus one has unbounded discrepancy along all homogeneous arithmetic progressions. We establish weighted variants of this problem, for weights given either by structured sequences that enjoy some irrationality features, or certain random sequences. As an intermediate result, we establish unboundedness of weighted sums of bounded multiplicative functions and products of shifts of such functions. A key ingredient in our analysis for the structured weights, is a structural result for measure preserving systems naturally associated with bounded multiplicative functions that was recently obtained in joint work with B. Host.
Publié le : 
@article{DAS_2020_a11,
     author = {Nikos Frantzikinakis},
     title = {Good weights for the {Erd\H{o}s} discrepancy problem},
     journal = {Discrete analysis},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DAS_2020_a11/}
}
TY  - JOUR
AU  - Nikos Frantzikinakis
TI  - Good weights for the Erdős discrepancy problem
JO  - Discrete analysis
PY  - 2020
UR  - http://geodesic.mathdoc.fr/item/DAS_2020_a11/
LA  - en
ID  - DAS_2020_a11
ER  - 
%0 Journal Article
%A Nikos Frantzikinakis
%T Good weights for the Erdős discrepancy problem
%J Discrete analysis
%D 2020
%U http://geodesic.mathdoc.fr/item/DAS_2020_a11/
%G en
%F DAS_2020_a11
Nikos Frantzikinakis. Good weights for the Erdős discrepancy problem. Discrete analysis (2020). http://geodesic.mathdoc.fr/item/DAS_2020_a11/