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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2022, Volume 62, Number 12, Pages 2002–2017
DOI: https://doi.org/10.31857/S0044466922120122 (Mi zvmmf11481) 		 
This article is cited in 1 scientific paper (total in 1 paper)

General numerical methods

Numerical investigation of the properties of remainder in Gauss's circle problem

D. A. Popova, D. V. Sushkob

a Belozersky Institute of Physico-Chemical Biology, 119992, Moscow, Russia
b Federal Research Center "Computer Science and Control", Russian Academy of Sciences, 119333, Moscow, Russia
Citations (1)
DOI: https://doi.org/10.31857/S0044466922120122
Abstract: Results of a numerical experiment on the investigation of the remainder in the problem about the number of integer points in a disk are presented. The pattern of behavior of large deviations of the remainder magnitude from zero is obtained. A numerical confirmation of the hypothesis on the width of maxima according to which all large local maxima of the remainder are fairly wide is obtained, and a hypothetical bound on the remainder magnitude is built. A theorem relating the height (value) of a remainder maximum with the width of this maximum is proved.
Key words: Gauss's circle problem, remainder, relation between the height and width of a maximum, numerical experiment, Landau's formula.
Received: 22.04.2022
Revised: 22.04.2022
Accepted: 04.06.2022
English version:
Computational Mathematics and Mathematical Physics, 2022, Volume 62, Issue 12, Pages 2008–2022
DOI: https://doi.org/10.1134/S0965542522120119
Bibliographic databases:
Document Type: Article
UDC: 511.338
Language: Russian
Citation: D. A. Popov, D. V. Sushko, “Numerical investigation of the properties of remainder in Gauss's circle problem”, Zh. Vychisl. Mat. Mat. Fiz., 62:12 (2022), 2002–2017; Comput. Math. Math. Phys., 62:12 (2022), 2008–2022
Citation in format AMSBIB
\Bibitem{PopSus22}
\by D.~A.~Popov, D.~V.~Sushko
\paper Numerical investigation of the properties of remainder in Gauss's circle problem
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2022
\vol 62
\issue 12
\pages 2002--2017
\mathnet{http://mi.mathnet.ru/zvmmf11481}
\crossref{https://doi.org/10.31857/S0044466922120122}
\elib{https://elibrary.ru/item.asp?id=49581397}
\transl
\jour Comput. Math. Math. Phys.
\yr 2022
\vol 62
\issue 12
\pages 2008--2022
\crossref{https://doi.org/10.1134/S0965542522120119}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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