TY - JOUR

T1 - On the distribution of kloosterman sums

AU - Shparlinski, Igor E.

N1 - 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

PY - 2008/2

Y1 - 2008/2

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=77950605600&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-07-08943-5

DO - 10.1090/S0002-9939-07-08943-5

M3 - Article

AN - SCOPUS:77950605600

SN - 0002-9939

VL - 136

SP - 419

EP - 425

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 2

ER -