Character sums with Beatty sequences on Burgess-type intervals
نویسندگان
چکیده
We estimate multiplicative character sums taken on the values of a non-homogeneous Beatty sequence {⌊αn + β⌋ : n = 1, 2, . . . }, where α, β ∈ R, and α is irrational. Our bounds are nontrivial over the same short intervals for which the classical character sum estimates of Burgess have been established. 2000 Mathematics Subject Classification: 11B50, 11L40, 11T24
منابع مشابه
Short Character Sums with Beatty Sequences
Abstract. We estimate multiplicative character sums taken on the values of a nonhomogeneous Beatty sequence {⌊αn+ β⌋ : n = 1, 2, . . . }, where α, β ∈ R, and α is irrational. In particular, our bounds imply that for fixed α, β and a small real number ε > 0, if p is sufficiently large and p1/3+ε ≤ N ≤ p1/2+ε, then among the first N elements of the Beatty sequence there are N/2+ o(N) quadratic no...
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