JournalszaaVol. 20, No. 4pp. 999–1006

L1L_1-Norms of Exponential Sums and the Corresponding Additive Problem

  • M.Z. Garaev

    Academia Sinica, Taipei, Taiwan
  • Ka-Lam Kueh

    Academia Sinica, Taipei, Taiwan
$L_1$-Norms of Exponential Sums and the Corresponding Additive Problem cover
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Abstract

In this note, a new estimate of L1L_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, L1L_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