Chowla's cosine problem
Classical Analysis and ODEs
2018-11-05 v2
Abstract
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.
Cite
@article{arxiv.0807.5104,
title = {Chowla's cosine problem},
author = {Tom Sanders},
journal= {arXiv preprint arXiv:0807.5104},
year = {2018}
}
Comments
21 pp. Corrected typos. Minor revisions