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Trudy Mat. Inst. Steklova, 2017, Volume 299, Pages 105–117 (Mi tm3823)  

This article is cited in 8 scientific papers (total in 8 papers)

Solution of functional equations related to elliptic functions

A. A. Illarionov

Khabarovsk Division of the Institute of Applied Mathematics, Far Eastern Branch of the Russian Academy of Sciences, ul. Dzerzhinskogo 54, Khabarovsk, 680000 Russia

Abstract: Functional equations of the form $f(x+y) g(x-y) = \sum _{j=1}^n \alpha _j(x)\beta _j(y)$ as well as of the form $f_1(x+z) f_2(y+z) f_3(x+y-z) = \sum _{j=1}^{m} \phi _j(x,y) \psi _j(z)$ are solved for unknown entire functions $f,g,\alpha _j,\beta _j: \mathbb{C} \to \mathbb{C} $ and $f_1,f_2,f_3,\psi _j: \mathbb{C} \to \mathbb{C} $, $\phi _j: \mathbb{C} ^2\to \mathbb{C} $ in the cases of $n=3$ and $m=4$.

Funding Agency Grant Number
Russian Science Foundation 14-11-00335
This work is supported by the Russian Science Foundation under grant 14-11-00335.


DOI: https://doi.org/10.1134/S0371968517040069

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English version:
Proceedings of the Steklov Institute of Mathematics, 2017, 299, 96–108

Bibliographic databases:

UDC: 517.965+517.583
Received: October 24, 2016

Citation: A. A. Illarionov, “Solution of functional equations related to elliptic functions”, Analytic number theory, On the occasion of the 80th anniversary of the birth of Anatolii Alekseevich Karatsuba, Trudy Mat. Inst. Steklova, 299, MAIK Nauka/Interperiodica, Moscow, 2017, 105–117; Proc. Steklov Inst. Math., 299 (2017), 96–108

Citation in format AMSBIB
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\by A.~A.~Illarionov
\paper Solution of functional equations related to elliptic functions
\inbook Analytic number theory
\bookinfo On the occasion of the 80th anniversary of the birth of Anatolii Alekseevich Karatsuba
\serial Trudy Mat. Inst. Steklova
\yr 2017
\vol 299
\pages 105--117
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3823}
\crossref{https://doi.org/10.1134/S0371968517040069}
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\jour Proc. Steklov Inst. Math.
\yr 2017
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\pages 96--108
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    This publication is cited in the following articles:
    1. A. A. Illarionov, M. A. Romanov, “Hyperquasipolynomials for the Theta-Function”, Funct. Anal. Appl., 52:3 (2018), 228–231  mathnet  crossref  crossref  mathscinet  isi  elib
    2. A. A. Illarionov, “On products of Weierstrass sigma functions”, J. Math. Sci. (N. Y.), 243:6 (2019), 872–879  mathnet  crossref
    3. A. A. Illarionov, “Reshenie funktsionalnykh uravnenii, svyazannykh s ellipticheskimi funktsiyami. II”, Sib. elektron. matem. izv., 16 (2019), 481–492  mathnet  crossref
    4. A. A. Illarionov, “Hyperelliptic systems of sequences of rank 4”, Sb. Math., 210:9 (2019), 1259–1287  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    5. A. V. Ustinov, “An Elementary Approach to the Study of Somos Sequences”, Proc. Steklov Inst. Math., 305 (2019), 305–317  mathnet  crossref  crossref  mathscinet  isi  elib
    6. A. A. Illarionov, “Asimmetrichnye kriptosistemy i giperellipticheskie posledovatelnosti”, Dalnevost. matem. zhurn., 19:2 (2019), 185–196  mathnet
    7. A. A. Illarionov, N. V. Markova, “Reshenie funktsionalnykh uravnenii, svyazannykh s ellipticheskimi funktsiyami. III”, Dalnevost. matem. zhurn., 19:2 (2019), 197–205  mathnet
    8. A. A. Illarionov, “On a Multilinear Functional Equation”, Math. Notes, 107:1 (2020), 80–92  mathnet  crossref  crossref  mathscinet  isi  elib
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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