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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2022, Volume 62, Number 7, Pages 1085–1099
DOI: https://doi.org/10.31857/S0044466922070055 (Mi zvmmf11421) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Ordinary differential equations

Summation of Poincaré theta series in the Schottky model

S. Yu. Lyamaev

Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, 119333, Moscow, Russia
Citations (1)
DOI: https://doi.org/10.31857/S0044466922070055
Abstract: New algorithms for approximate summation of Poincaré theta series in the Schottky model of real hyperelliptic curves are proposed. As a result, for the same output accuracy estimate, the amount of computations is reduced by several times in the case of slow convergence and by tens of percent in the usual situations. For the sum of the Poincaré series over the subtree on descendants of a given node, a new estimate in terms of the series member at this node is obtained.
Key words: Schottky groups, Poincaré theta series, Cayley graph, uniformization, real hyperelliptic curves, Riemann surfaces.
Funding agency Grant number
Moscow Center of Fundamental and Applied Mathematics 075-15-2019-1624
Russian Science Foundation 21-11-00325
The research concerning the new estimate for the sum of the Poincaré series was supported by the Moscow Center for Fundamental and Applied Mathematics, Department at the Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences (agreement no. 075-15-2019-1624). The rest of this study was supported by the Russian Science Foundation, grant no. 21-11-00325.
Received: 30.11.2021
Revised: 13.02.2022
Accepted: 11.03.2022
English version:
Computational Mathematics and Mathematical Physics, 2022, Volume 62, Issue 7, Pages 1059–1073
DOI: https://doi.org/10.1134/S0965542522070053
Bibliographic databases:
Document Type: Article
UDC: 517.545
Language: Russian
Citation: S. Yu. Lyamaev, “Summation of Poincaré theta series in the Schottky model”, Zh. Vychisl. Mat. Mat. Fiz., 62:7 (2022), 1085–1099; Comput. Math. Math. Phys., 62:7 (2022), 1059–1073
Citation in format AMSBIB
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\by S.~Yu.~Lyamaev
\paper Summation of Poincar\'e theta series in the Schottky model
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2022
\vol 62
\issue 7
\pages 1085--1099
\mathnet{http://mi.mathnet.ru/zvmmf11421}
\crossref{https://doi.org/10.31857/S0044466922070055}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4466932}
\elib{https://elibrary.ru/item.asp?id=48621819}
\transl
\jour Comput. Math. Math. Phys.
\yr 2022
\vol 62
\issue 7
\pages 1059--1073
\crossref{https://doi.org/10.1134/S0965542522070053}
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  • https://www.mathnet.ru/eng/zvmmf/v62/i7/p1085
    • 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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