a1 Department of Mathematics, University of Missouri, Columbia, MO 65211, United States of America, e-mail: email@example.com
a2 Department of Computing, Macquarie University, Sydney, NSW 2109, Australia, e-mail: firstname.lastname@example.org
We study multiplicative character sums taken on the values of a non-homogeneous Beatty sequence where α,β , and α is irrational. In particular, our bounds imply that for every fixed ε > 0, if p is sufficiently large and p½+ε ≤ N ≤ p, then among the first N elements of α,β, there are N/2+o(N) quadratic non-residues modulo p. When more information is available about the Diophantine properties of α, then the error term o(N) admits a sharper estimate.
(Received January 31 2006)