Well Distribution of Sidon Sets in Residue Classes

The Distribution of Sequences in Residue Classes

We prove that any set of integers A ⊂ [1, x] with |A| (log x)r lies in at least νA(p) p r r+1 many residue classes modulo most primes p (log x)r+1. (Here r is a positive constant.) This generalizes a result of Erdős and Ram Murty, who proved in connection with Artin’s conjecture on primitive roots that the integers below x which are multiplicatively generated by the coprime integers a1, . . . ,...

Sumsets of Sidon sets

Sidon Sets in N

We study finite and infinite Sidon sets in N. 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. We also disprove a conjecture of Lindstrom on the largest Sidon set in [1, N ]× [1, N ] and relate it to a known conjecture of Vinogradov concerning the size of the...

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

Arithmetic Characterizations of Sidon Sets

Let G be any discrete Abelian group. We give several arithmetic characterizations of Sidon sets in G. In particular, we show that a set A is a Sidon set iff there is a number 6 > 0 such that any finite subset A of A contains a subset B Q A with |B| > 6\A\ which is quasiindependent, i.e. such that the only relation of the form ]C\eB e x ^ = '̂ with e\ equal to + 1 or 0, is the trivial one. Let G ...