On the distribution of kloosterman sums

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Abstract

For a prime p, we consider Kloosterman sums over a finite field of pelements. It is well known that due to results of Deligne, Katz and Sarnak, the distribution of the sums Kp (a)when a runs through F p* is in accordance with the Sato-Tate conjecture. Here we show that the same holds where a runs through the sums a = u + v for u εU, v εV for any two sufficiently large sets U, V⊆ Fp.* We also improve a recent bound on the nonlinearity of a Boolean function associated with the sequence of signs of Kloosterman sums.

Original languageEnglish
Pages (from-to)419-425
Number of pages7
JournalProceedings of the American Mathematical Society
Volume136
Issue number2
DOIs
Publication statusPublished - Feb 2008

Bibliographical note

Copyright 2008 American Mathematical Society. First published in Proceedings of the American Mathematical Society, vol 136, Iss 2, published by the American Mathematical Society. The original article can be found at http://dx.doi.org/10.1090/S0002-9939-07-08943-5

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