INTEGRAL EQUATION FOR THE NUMBER OF INTEGER POINTS IN A CIRCLE

Authors

  • Magomed A. Chakhkiev Social State University of Russia - Department of Applied Mathematics
  • Gagik S. Sulyan Social State University of Russia - Department of Applied Mathematics
  • Manya A. Ziroyan Social State University of Russia - Department of Applied Mathematics
  • Nikolay P. Tretyakov Social State University of Russia - Department of Applied Mathematics
  • Saif A. Mouhammad Taif University - Department of Physics

Keywords:

Gauss circle problem, integral equation, Hankel transform

Abstract

The problem is to obtain the most accurate upper estimate for the absolute value of the difference between the number of integer points in a circle and its area (when the radius tends to infinity).  In this paper we obtain an integral equation for the function expressing the dependence of the number of integer points in a circle on its radius.  The kernel of the equation contains the Bessel functions of the first kind, and the equation itself is a kind of the Hankel transform.

Cover of n°41 Italian Journal of Pure and Applied Mathematics

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Published

2019-02-27

How to Cite

Chakhkiev, M. A., Sulyan, G. S., Ziroyan, M. A., Tretyakov, N. P., & Mouhammad, S. A. (2019). INTEGRAL EQUATION FOR THE NUMBER OF INTEGER POINTS IN A CIRCLE. Italian Journal of Pure and Applied Mathematics, 41, 522–525. Retrieved from https://journals.uniurb.it/index.php/ijpam/article/view/7094

Issue

N°41 - February 2019

Section

Articoli - Forum Editrice

License

Copyright (c) 2019 Magomed A. Chakhkiev, Gagik S. Sulyan, Manya A. Ziroyan, Nikolay P. Tretyakov, Saif A. Mouhammad

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

L'opera è pubblicata sotto  Licenza Creative Commons Attribuzione 4.0 Internazionale (CC-BY)

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