Lattice Points in Many-Dimensional Balls
- Authors: Fomenko O.M.1
-
Affiliations:
- St.Petersburg Department of the Steklov Mathematical Institute
- Issue: Vol 225, No 6 (2017)
- Pages: 1012-1021
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/239897
- DOI: https://doi.org/10.1007/s10958-017-3512-3
- ID: 239897
Cite item
Abstract
Let Pk(n) be the difference between the number of points of the integer lattice contained in the ball \( {y}_1^2+\cdots {y}_k^2\le n \) and the volume of this ball. The paper investigates the asymptotic behavior of
the sums
\( \sum_{n\le x}{P}_k(n)\kern0.5em \left(k\ge 4\right),\kern0.5em \sum_{n\le x}{P}_3^2(n),\kern0.5em \sum_{n\le x}{P}_4^2(n)\kern1em as\kern0.5em x\to +\infty . \)
About the authors
O. M. Fomenko
St.Petersburg Department of the Steklov Mathematical Institute
Author for correspondence.
Email: fomenko@pdmi.ras.ru
Russian Federation, St. Petersburg