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Mat. Sb., 2019, Volume 210, Number 9, Pages 59–88 (Mi msb9050)  

This article is cited in 3 scientific papers (total in 3 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

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 ${f(x+y)f(x-y)}=\varphi_1(x)\psi_1(y)+…+\varphi_4(x)\psi_4(y)$ 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).


DOI: https://doi.org/10.4213/sm9050

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English version:
Sbornik: Mathematics, 2019, 210:9, 1259–1287

Bibliographic databases:

UDC: 517.965+517.583
MSC: Primary 11B83, 39B32; Secondary 11B37
Received: 15.12.2017 and 10.04.2019

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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  • https://doi.org/10.4213/sm9050
  • http://mi.mathnet.ru/eng/msb/v210/i9/p59

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. A. Illarionov, “Asimmetrichnye kriptosistemy i giperellipticheskie posledovatelnosti”, Dalnevost. matem. zhurn., 19:2 (2019), 185–196  mathnet
    2. A. A. Illarionov, N. V. Markova, “Reshenie funktsionalnykh uravnenii, svyazannykh s ellipticheskimi funktsiyami. III”, Dalnevost. matem. zhurn., 19:2 (2019), 197–205  mathnet
    3. A. A. Illarionov, “On a Multilinear Functional Equation”, Math. Notes, 107:1 (2020), 80–92  mathnet  crossref  crossref  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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