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Dal'nevost. Mat. Zh., 2017, Volume 17, Number 2, Pages 210–220 (Mi dvmg355)  

This article is cited in 1 scientific paper (total in 1 paper)

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

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


Full text: PDF file (572 kB)
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Document Type: Article
UDC: 517.965+517.547.582+511.21
MSC: Primary 33E05; Secondary 11B37
Received: 26.10.2017

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{http://elibrary.ru/item.asp?id=32239884}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. A. Illarionov, “O proizvedenii dvukh sigma-funktsii Veiershtrassa”, Issledovaniya po lineinym operatoram i teorii funktsii. 46, Zap. nauchn. sem. POMI, 467, POMI, SPb., 2018, 73–84  mathnet
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