On the general additive divisor problem |
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| Authors: | Aleksandar Ivić Jie Wu |
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| Institution: | 1.Katedra Matematike, Rudarsko-geolo?ki Fakultet,Universitet u Beogradu,Beograd,Serbia;2.School of Mathematics,Shandong University,Jinan, Shandong,China;3.Institut élie Cartan Nancy, CNRS,Université Henri Poincaré (Nancy 1), INRIA,Vand?uvre-lès-Nancy,France |
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| Abstract: | We obtain a new upper bound for the sum Σ
h≤H
Δ
k
(N, h) when 1 ≤ H ≤ N, k ∈ ℕ, k ≥ 3, where Δ
k
(N, h) is the (expected) error term in the asymptotic formula for Σ
N<n≤2N
d
k
(n)d
k
(n + h), and d
k
(n) is the divisor function generated by ζ(s)
k
. When k = 3, the result improves, for H ≥ N
1/2, the bound given in a recent work of Baier, Browning, Marasingha and Zhao, who dealt with the case k = 3. |
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| Keywords: | |
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