Representation functions, Sidon sets and bases

On Sidon sets and asymptotic bases

Erdős conjectured the existence of an infinite Sidon sequence of positive integers which is an asymptotic basis of order 3. We progress towards this conjecture in several directions. We prove the conjecture for all cyclic groups ZN with N large enough. We also show that there is an infinite B2[2] sequence which is an asymptotic basis of order 3. Finally, we prove that for any ε > 0 there is a S...

Generalized Sidon sets

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. © 2010 Elsevier Inc. All rights reserved. MSC: 11B

Sumsets of Sidon sets

Sidon sets and Riesz products

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Perfect difference sets constructed from Sidon sets

A set A of positive integers is a perfect difference set if every nonzero integer has an unique representation as the difference of two elements of A. We construct dense perfect difference sets from dense Sidon sets. As a consequence of this new approach we prove that there exists a perfect difference set A such that A(x) ≫ x √ . Also we prove that there exists a perfect difference set A such t...