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Dal'nevostochnyi Matematicheskii Zhurnal, 2017, Volume 17, Number 2, Pages 210–220 (Mi dvmg355)  
This article is cited in 3 scientific papers (total in 3 papers)

On the connection between hyperelliptic systems of sequences and functions

A. A. Illarionovab, M. A. Romanova

a Khabarovsk Division of the Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences
b Pacific National University, Khabarovsk
Full-text PDF (572 kB) Citations (3)
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Abstract: We study the connection between $1$-periodic solutions of the functional equation
$$ f(x+y)g(x-y)=\sum_{j=1}^N\varphi_j(x)\psi_j(y) \quad (x,y\in \mathbb C) $$
and some sequences of special kind. As an application we solve the equation in the case when $g$ is Jacobi theta function.
Key words: functional equation, Weierstrass sigma function, Jacobi theta function, addition formula, elliptic functions, nonlinear sequences.
Funding agency Grant number
Russian Foundation for Basic Research 17-01-00225
Received: 26.10.2017
Bibliographic databases:
Document Type: Article
UDC: 517.965+517.547.582+511.21
MSC: Primary 33E05; Secondary 11B37
Language: Russian
Citation: A. A. Illarionov, M. A. Romanov, “On the connection between hyperelliptic systems of sequences and functions”, Dal'nevost. Mat. Zh., 17:2 (2017), 210–220
Citation in format AMSBIB
\Bibitem{IllRom17}
\by A.~A.~Illarionov, M.~A.~Romanov
\paper On the connection between hyperelliptic systems of sequences and functions
\jour Dal'nevost. Mat. Zh.
\yr 2017
\vol 17
\issue 2
\pages 210--220
\mathnet{http://mi.mathnet.ru/dvmg355}
\elib{https://elibrary.ru/item.asp?id=32239884}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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