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$p$-Rider sets are $q$-Sidon sets

Authors: P. Lefèvre and L. Rodríguez-Piazza
Journal: Proc. Amer. Math. Soc. 131 (2003), 1829-1838
MSC (2000): Primary 43A46
Published electronically: October 1, 2002
MathSciNet review: 1955271
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Abstract: The aim of this paper is to prove that for every $p<{\frac43}$, every $p$-Rider set is a $q$-Sidon set for all $q>{\frac p{2-p}}\cdot$ This gives some positive answers for the union problem of $p$-Sidon sets. We also obtain some results on the behavior of the Fourier coefficient of a measure with spectrum in a $p$-Rider set.

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Additional Information

P. Lefèvre
Affiliation: Université d’Artois, Faculté Jean Perrin, rue Jean Souvraz S.P. 18 62307 Lens cedex, France

L. Rodríguez-Piazza
Affiliation: Universidad de Sevilla, Faculdad de Matematica, Apdo 1160, 41080 Sevilla, Spain

Keywords: $p$-Sidon-ps, $p$-Rider set, $q$-Sidon set, quasi-independent sets, random Fourier series
Received by editor(s): June 21, 2001
Received by editor(s) in revised form: January 24, 2002
Published electronically: October 1, 2002
Communicated by: Andreas Seeger
Article copyright: © Copyright 2002 American Mathematical Society