On the binary additive divisor problem in mean

: Eeva Vehkalahti (née Suvitie)

: 2017

Journal of Number Theory

: JOURNAL OF NUMBER THEORY

: J NUMBER THEORY

: 177

: 428

: 442

: 15

: 0022-314X

: 1096-1658

DOI: https://doi.org/10.1016/j.jnt.2017.01.016

We study a mean value of the classical additive divisor problem, that isSigma(f similar to F) Sigma(n similar to N)vertical bar Sigma(l similar to L) d(n + l)d(n +l+ f) - main term vertical bar(2) ,with quantities N >= 1, 1 <= F "N1-epsilon and 1 <= L <= N. The main term we are interested in here is the one by Motohashi [27], but we also give an upper bound for the case where the main term is that of Atkinson [1]. Furthermore, we point out that the proof yields an analogous upper bound for a shifted convolution sum over Fourier coefficients of a fixed holomorphic cusp form in mean. (C) 2017 Elsevier Inc. All rights reserved.