On the binary additive divisor problem in mean

2011/10/18 by Eeva Suvitie, Suvitie, Eeva
Mathematics · #11F72 (Secondary) #11N37 (Primary) 11F30 #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1110.3950

openalex publication_date 2011/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a mean value of the classical additive divisor problem. The main term we are interested in here is the one by Motohashi, but we also give an upper bound for the case where the main term is that of Atkinson. 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.

Related

• A note on the binary additive divisor problem
• On binary and quadratic divisor problems
• Additive divisor problem for multiplicative functions
• On the mean square of the error term for the two-dimensional divisor problems(II)
• Asymptotic identities for additive convolutions of sums of divisors