# Generalized sidon sets

@article{Cilleruelo2009GeneralizedSS,
title={Generalized sidon sets},
author={Javier Cilleruelo and Imre Z. Ruzsa and Carlos Vinuesa},
year={2009},
volume={225},
pages={2786-2807}
}
• Published 2009
• Mathematics
We give asymptotic sharp estimates for the cardinality of a set of residue classes with the property that the representation function is bounded by a prescribed number. We then use this to obtain an analogous result for sets of integers, answering an old question of Simon Sidon.
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Sidon sets in Nd
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The additive energy of two sets is used to obtain new upper bounds for the cardinalities of finite Sidon subsets of some sets as well as to provide short proofs of already known results. Expand