Chowla's cosine problem

Details Chowla's cosine problem Chowla's cosine problem

2008-07-31

arxiv.org/abs/0807.5104v2

Israel J. Math. 179 (2010), 1-28

Mathematics

Classical Analysis and ODEs

21 pp. Corrected typos. Minor revisions

Scientific paper

Suppose that G is a discrete abelian group and A is a finite symmetric subset of G. We show two main results. i) Either there is a set H of O(log^c|A|) subgroups of G with |A \triangle \bigcup H| = o(|A|), or there is a character X on G such that -wh{1_A}(X) >> log^c|A|. ii) If G is finite and |A|>> |G| then either there is a subgroup H of G such that |A \triangle H| = o(|A|), or there is a character X on G such that -wh{1_A}(X)>> |A|^c.

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