Abstract:
An elementary approach (not involving the theory of elliptic functions) is proposed to the proof of the main properties of the Somos-4 sequence.
Citation:
A. V. Ustinov, “An Elementary Approach to the Study of Somos Sequences”, Algebraic topology, combinatorics, and mathematical physics, Collected papers. Dedicated to Victor Matveevich Buchstaber, Corresponding Member of the Russian Academy of Sciences, on the occasion of his 75th birthday, Trudy Mat. Inst. Steklova, 305, Steklov Math. Inst. RAS, Moscow, 2019, 330–343; Proc. Steklov Inst. Math., 305 (2019), 305–317
\Bibitem{Ust19}
\by A.~V.~Ustinov
\paper An Elementary Approach to the Study of Somos Sequences
\inbook Algebraic topology, combinatorics, and mathematical physics
\bookinfo Collected papers. Dedicated to Victor Matveevich Buchstaber, Corresponding Member of the Russian Academy of Sciences, on the occasion of his 75th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2019
\vol 305
\pages 330--343
\publ Steklov Math. Inst. RAS
\publaddr Moscow
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\crossref{https://doi.org/10.4213/tm3990}
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\transl
\jour Proc. Steklov Inst. Math.
\yr 2019
\vol 305
\pages 305--317
\crossref{https://doi.org/10.1134/S0081543819030180}
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Linking options:
https://www.mathnet.ru/eng/tm3990
https://doi.org/10.4213/tm3990
https://www.mathnet.ru/eng/tm/v305/p330
This publication is cited in the following 4 articles:
A. V. Ustinov, “On Periodicity of the Somos Sequences Modulo m”, Math. Notes, 115:3 (2024), 405–413
A. A. Illarionov, “Existence of sequences satisfying bilinear type recurrence relations”, Problems Inform. Transmission, 59:2 (2023), 163–180
V. A. Bykovskii, M. A. Romanov, “Polynomial Somos Sequences”, Funct. Anal. Appl., 55:1 (2021), 15–25
A. V. Ustinov, “On Somos-4 and Somos-5 Sequences”, Math. Notes, 110:3 (2021), 470–472