$L_1$-Norms of Exponential Sums and the Corresponding Additive Problem
$L_1$-Norms of Exponential Sums and the Corresponding Additive Problem
In this note, a new estimate of L_1 -norm of certain exponential sum is obtained. At the same time, we establish a sharp lower bound for the cardinality of corresponding sumsets. In some cases this lower bound gives the true order of the cardinality.