On sets of large exponential sums
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 (r1, r2, r3, r4) ∈ R4 such that r1 + r2 = r3 + r4 is at least |R|2+ε, ε>0. This statement shows that the set R is highly structured. We also discuss some of the generalizations and applications of our result.
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