On a variance associated with the distribution of r₃(n) in arithmetic progressions

2020/10/09 by Pengyong Ding, Ding, Pengyong
Mathematics · #11N37 (Primary) 11B57 #11P55 (Secondary) #Analytic Number Theory Research #FOS: Mathematics #History and Theory of Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2010.04319

openalex publication_date 2020/10/09 · openalex created_date 2020/10/15 · openalex updated_date 2026/07/28

Abstract

There are two questions in analytic number theory which have attracted much attention over the years. The first one is about the asymptotic formula for the variance associated with the distribution of a real sequence in arithmetic progressions, which origins in the work of Barban. The second one is about the function r₃(n), the number of ordered representation of n in the sum of three positive cubes, and several results are recently proved by Robert C. Vaughan. The paper is concerned with the conjunction of these questions, with the application of the Hardy-Littlewood Method and the Farey sequence.

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