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

M.Z. Garaev; Ka-Lam Kueh

doi:10.4171/zaa/1056

JournalszaaVol. 20, No. 4pp. 999–1006

$L_{1}$ -Norms of Exponential Sums and the Corresponding Additive Problem

M.Z. Garaev
Academia Sinica, Taipei, Taiwan
Ka-Lam Kueh
Academia Sinica, Taipei, Taiwan

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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