Non-residues and primitive roots in Beatty sequences
2006 ◽
Vol 73
(3)
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pp. 433-443
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Keyword(s):
We study multiplicative character sums taken on the values of a non-homogeneous Beatty sequence 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 p½+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) admits a sharper estimate.
2019 ◽
Vol 8
(6S3)
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pp. 115-118
2018 ◽
Vol 2020
(10)
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pp. 2881-2917
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2010 ◽
Vol 53
(1)
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pp. 1-12
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2021 ◽
Vol 314
(1)
◽
pp. 64-89
Keyword(s):
2014 ◽
Vol 90
(3)
◽
pp. 376-390
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2011 ◽
Vol 07
(06)
◽
pp. 1557-1571
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2008 ◽
Vol 50
(3)
◽
pp. 523-529
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