On sets of large exponential sums
Number Theory
2007-05-23 v1 Combinatorics
Abstract
Let A be a subset of Z / NZ, and let R be the set of large Fourier coefficients of A. Properties of R have been studied in works of M.-C. Chang and B. Green. Our result is the following : the number of quadruples (r_1, r_2, r_3, r_4) \in R^4 such that r_1 + r_2 = r_3 + r_4 is at least |R|^{2+\epsilon}, \epsilon>0. This statement shows that the set R is highly structured. We also discuss some of the generalizations and applications of our result.
Cite
@article{arxiv.math/0605689,
title = {On sets of large exponential sums},
author = {I. D. Shkredov},
journal= {arXiv preprint arXiv:math/0605689},
year = {2007}
}
Comments
19 pages