Combinatorial problems in finite fields and Sidon sets

Combinatorial problems in finite fields and Sidon sets

We use Sidon sets to present an elementary method to study some combinatorial problems in finite fields, such as sum product estimates, solvability of some equations and the distribution of their solutions. We obtain classic and more recent results avoiding the use of exponential sums, the usual tool to deal with these problems.

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

Sumsets of Sidon sets

Sidon sets and Riesz products

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