A1 Refereed original research article in a scientific journal
On the binary additive divisor problem in mean
Authors: Eeva Vehkalahti (née Suvitie)
Publisher: ACADEMIC PRESS INC ELSEVIER SCIENCE
Publication year: 2017
Journal: Journal of Number Theory
Journal name in source: JOURNAL OF NUMBER THEORY
Journal acronym: J NUMBER THEORY
Volume: 177
First page : 428
Last page: 442
Number of pages: 15
ISSN: 0022-314X
eISSN: 1096-1658
DOI: https://doi.org/10.1016/j.jnt.2017.01.016
Abstract
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.
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.
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