A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
On the binary additive divisor problem in mean
Tekijät: Eeva Vehkalahti (née Suvitie)
Kustantaja: ACADEMIC PRESS INC ELSEVIER SCIENCE
Julkaisuvuosi: 2017
Lehti: Journal of Number Theory
Tietokannassa oleva lehden nimi: JOURNAL OF NUMBER THEORY
Lehden akronyymi: J NUMBER THEORY
Vuosikerta: 177
Aloitussivu: 428
Lopetussivu: 442
Sivujen määrä: 15
ISSN: 0022-314X
eISSN: 1096-1658
DOI: https://doi.org/10.1016/j.jnt.2017.01.016
Tiivistelmä
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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