Article
On the Sum of Bounded Multiplicative Functions over Some Special Subsets of Integers
Authors
Abstract
Let J1, . . . , J k ⊆ [0, 1) be finite unions of intervals, P1(x), . . . , P k (x) ∈ R[x] of degree at least one, Qm1,...,mk (x) = m1P1(x) + . . . + m k P k (x), m1, . . . , m k ∈ Z. Assume that Qm1,...,mk (x) − Qm1,...,mk (0) has at least one irrational coeffi- cient for every (m1, . . . , m k )= (0, . . . , 0). Let S := {n | n ∈ N, {P (n)} ∈ J , l = 1, . . . , k}, λ = Lebesgue measure. We l l shall prove the following theorem. Under the conditions stated aboveg∈ su M p 1x 1 n≤x g(n) − λ(J1) . . x . (λ(J k ) n≤x g(n)= τx → 0 n∈ S as x → ∞. Here M1 is the set of complex valued multiplicative functions g satisfying |g(n)| ≤ 1 (n ∈ N).
Keywords
Almost periodic functions, trigonometric sums, theorem of Daboussi, Beatty.
Citation
Katai, I. (2008). On the sum of bounded multiplicative functions over some special subsets of integers. Uniform Distribution Theory, 3(2), 37–43.
I. Katai, “On the sum of bounded multiplicative functions over some special subsets of integers,” Uniform Distribution Theory, vol. 3, no. 2, pp. 37–43, 2008.
Katai I. On the sum of bounded multiplicative functions over some special subsets of integers. Uniform Distribution Theory. 2008;3(2):37–43.
Katai, I. (2008), ‘On the sum of bounded multiplicative functions over some special subsets of integers’, Uniform Distribution Theory, 3(2), pp. 37–43.
Katai, Imre. “On the Sum of Bounded Multiplicative Functions Over Some Special Subsets of Integers.” Uniform Distribution Theory, vol. 3, no. 2, 2008, pp. 37–43.
Katai, Imre. “On the Sum of Bounded Multiplicative Functions Over Some Special Subsets of Integers.” Uniform Distribution Theory 3, no. 2 (2008): 37–43.
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Published by: Engineering Journals
