New pseudorandom sequences constructed by quadratic residues and Lehmer numbers

作者:Liu Huaning*
来源:Proceedings of the American Mathematical Society, 2007, 135(5): 1309-1318.
DOI:10.1090/S0002-9939-06-08630-8

摘要

Let p be an odd prime. Define
e(n) = {(-1)(n+n), if n is a quadratic residue mod p, (-1)(n+n+1), if n is a quadratic nonresidue mod p,
where n is the multiplicative inverse of n modulo p such that 1 <= n <= p - 1. This paper shows that the sequence {e(n)} is a "good" pseudorandom sequence, by using the properties of exponential sums, character sums, Kloosterman sums and mean value theorems of Dirichlet L-functions.