Non-residues and primitive roots in Beatty sequences

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Non-residues and primitive roots in Beatty sequences

Please use this identifier to cite or link to this item: http://hdl.handle.net/10355/10850

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Title: Non-residues and primitive roots in Beatty sequences
Author: Banks, William David, 1964-; Shparlinski, Igor E.
Date: 2006
Publisher: Australian Mathematical Society
Citation: Bull. Austral. Math. Soc. 73 (2006), 433-443.
Abstract: We study multiplicative character sums taken on the values of a non-homogeneous Beatty sequence Bα,β = {⌊αn + β⌋ : n = 1,2,3,…}, where α,β ∈ R, and α is irrational. In particular, our bounds imply that for every fixed ε > 0, if p is sufficiently large and p1/2+ε ≤ N ≤ p, then among the first N elements of Bα,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) emits a shaper estimate.
URI: http://hdl.handle.net/10355/10850
ISSN: 0004-9727

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