On the general additive divisor problem

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 ≤2 N 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 impr...

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Veröffentlicht in:	Proceedings of the Steklov Institute of Mathematics 2012-04, Vol.276 (1), p.140-148
Hauptverfasser:	Ivić, Aleksandar, Wu, Jie
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Sprache:	eng
Schlagworte:	Mathematics Mathematics and Statistics Number Theory
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container_title	Proceedings of the Steklov Institute of Mathematics
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creator	Ivić, Aleksandar Wu, Jie
description	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 ≤2 N 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.
doi_str_mv	10.1134/S0081543812010117
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title	On the general additive divisor problem
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