On sets of large exponential sums

Some examples of sets of large exponential sums ∗

Let A be a subset of Z/N Z and let R be the set of large Fourier coefficients of A. Properties of R have been studied in works of M.– C. Chang, B. Green and the author. In the paper we obtain some new results on sets of large exponential sums.

M ay 2 00 6 On sets of large exponential sums , I ∗

Let A be a subset of Z/N Z 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) ∈ R 4 such that r 1 + r 2 = r 3 + r 4 is at least |R| 2+ǫ , ǫ > 0. This statement shows that the set R is highly structured. We also discuss some of the generali...

on direct sums of baer modules

the notion of baer modules was defined recently

Exponential Sums on A

Let d = degree of f and write f = f (d) + f (d−1) + · · ·+ f , where f (j) is homogeneous of degree j. A by now classical theorem of Deligne[2, Théorème 8.4] says that if (p, d) = 1 and f (d) = 0 defines a smooth hypersurface in P, then L(A, f ; t) n+1 is a polynomial of degree (d − 1), all of whose reciprocal roots have absolute value equal to q. This implies the estimate |S(A(Fqi), f)| ≤ (d− ...

On Exponential Sums