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Sbornik: Mathematics, 2019, Volume 210, Issue 9, Pages 1259–1287
DOI: https://doi.org/10.1070/SM9050 (Mi sm9050) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Hyperelliptic systems of sequences of rank 4

A. A. Illarionovab

a Khabarovsk Division of the Institute for Applied Mathematics, Far Eastern Branch of the Russian Academy of Sciences, Khabarovsk, Russia
b Pacific National University, Khabarovsk, Russia
English version PDF (611 kB) Citations (8)
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DOI: https://doi.org/10.1070/SM9050
Abstract: Sequences of complex numbers satisfying functional relations of bilinear type are investigated. The results obtained are used in describing all 1-periodic entire functions $f\colon \mathbb C\to\mathbb C$ such that the expansion ${f(x+y)f(x-y)}=\varphi_1(x)\psi_1(y)+\dots+\varphi_4(x)\psi_4(y)$ holds for some $\varphi_j,\psi_j\colon\mathbb C\to\mathbb C$.
Bibliography: 38 titles.
Keywords: addition theorems, elliptic functions, functional equations, nonlinear recurrent sequences.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00638-а
This research was carried out with the support of the Russian Foundation for Basic Research (grant no. 18-01-00638-a).
Received: 15.12.2017 and 10.04.2019
Russian version:
Matematicheskii Sbornik, 2019, Volume 210, Number 9, Pages 59–88
DOI: https://doi.org/10.4213/sm9050
Bibliographic databases:
Document Type: Article
UDC: 517.965+517.583
MSC: Primary 11B83, 39B32; Secondary 11B37
Language: English
Original paper language: Russian
Citation: A. A. Illarionov, “Hyperelliptic systems of sequences of rank 4”, Mat. Sb., 210:9 (2019), 59–88; Sb. Math., 210:9 (2019), 1259–1287
Citation in format AMSBIB
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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