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 -