# $L_1$-Norms of Exponential Sums and the Corresponding Additive Problem

### M.Z. Garaev

Academia Sinica, Taipei, Taiwan### Ka-Lam Kueh

Academia Sinica, Taipei, Taiwan

## Abstract

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.

## Cite this article

M.Z. Garaev, Ka-Lam Kueh, $L_1$-Norms of Exponential Sums and the Corresponding Additive Problem. Z. Anal. Anwend. 20 (2001), no. 4, pp. 999–1006

DOI 10.4171/ZAA/1056