On a variance associated with the distribution of real sequences in arithmetic progressions
Volume 211 / 2023
Acta Arithmetica 211 (2023), 229-263
MSC: Primary 11N64; Secondary 11P55.
DOI: 10.4064/aa221003-14-8
Published online: 30 October 2023
Abstract
This article is composed of two parts. The first part concerns the general result on the variance associated with the distribution of a real sequence $\{a_n\}$ over arithmetic progressions, and the second part is an example of calculating the variance when $a_n=r_3(n)$, the number of (ordered) representations of $n$ as the sum of three positive cubes.
