On the general additive divisor problem

2011/06/23 by Ivic, Aleksandar, Wu, Jie · 1 citation
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1106.4744

Abstract

We obtain a new upper bound for ∑_{h≤ H}Δ_k(N,h) for 1≤ H≤ N, k∈ \N, k≥3, where Δ_k(N,h) is the (expected) error term in the asymptotic formula for ∑_{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 the recent work \cite[1] of Baier, Browning, Marasingha and Zhao, who dealt with the case k=3.

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