Type: Article

On an additive representation associated with the L_1-norm of an exponential sum

M. Z. Garaev;

Abstract:

Let N be a large positive integer parameter, f(n) be an integer valued strictly increasing function of the natural argument n. It is well known that a nontrivial upper bound estimate for the number of solutions of the diophantine equation f(x) + f(y) = f(u) + f(v), 1 <= x,y,u,v <= N has an important application in obtaining a lower bound for the L-1-norm of an exponential sum. In this paper by a short argument we obtain a result which implies a well-known estimate of Konyagin.