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Zeitschrift für Analysis und ihre Anwendungen

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Volume 20, Issue 4, 2001, pp. 999–1006
DOI: 10.4171/ZAA/1056

Published online: 2001-12-31

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

M.Z. Garaev[1] and Ka-Lam Kueh[2]

(1) Academia Sinica, Taipei, Taiwan
(2) Academia Sinica, Taipei, Taiwan

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.

Keywords: $L_1$-norms, exponential sums, cardinality of sumsets

Garaev M.Z., Kueh Ka-Lam: $L_1$-Norms of Exponential Sums and the Corresponding Additive Problem. Z. Anal. Anwend. 20 (2001), 999-1006. doi: 10.4171/ZAA/1056