A. A. Illarionov, “On the Somos-4 sequence”, Dal'nevost. Mat. Zh., 18:2 (2018), 183

Dal'nevostochnyi Matematicheskii Zhurnal

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	General information
	Latest issue
	Archive
	Impact factor
	Submit a manuscript

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

Dal'nevost. Mat. Zh.:
Year:
Volume:
Issue:
Page:
	Find

Personal entry:
Login:
Password:
	Save password
	Enter
	Forgotten password?
	Register

Dal'nevostochnyi Matematicheskii Zhurnal, 2018, Volume 18, Number 2, Pages 183–188 (Mi dvmg379)

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

On the Somos-4 sequence

A. A. Illarionov^ab

^a Khabarovsk Division of the Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences
^b Pacific National University, Khabarovsk

Full-text PDF (483 kB) Citations (3)

References:

PDF

HTML

Abstract: In 2005 A.N.W. Hone has obtained an explicit formula for Somos-4 sequences in terms of the Weierstrass sigma function. The proof is valid only for sequences without zero terms. We prove that arbitrary sequence satisfying the Somos-4 equation is determined by the same formula iff it satisfies some determinant identity (analogue of the formula of addition). We give examples of sequences that satisfy the Somos-4 equation but do not satisfy the determinant identity.

Key words: Somos sequences, elliptic functions, addition theorems.

Funding agency	Grant number
Russian Foundation for Basic Research	18-01-00638

Received: 16.10.2018

Document Type: Article

UDC: 517.52+512.742.72

MSC: Primary 11B37; Secondary 33E05

Language: Russian

Citation: A. A. Illarionov, “On the Somos-4 sequence”, Dal'nevost. Mat. Zh., 18:2 (2018), 183–188

Citation in format AMSBIB

\Bibitem{Ill18}

\by A.~A.~Illarionov

\paper On the Somos-4 sequence

\jour Dal'nevost. Mat. Zh.

\yr 2018

\vol 18

\issue 2

\pages 183--188

\mathnet{http://mi.mathnet.ru/dvmg379}

Linking options:

https://www.mathnet.ru/eng/dvmg379

https://www.mathnet.ru/eng/dvmg/v18/i2/p183

This publication is cited in the following 3 articles:

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

Statistics & downloads:
Abstract page:	278
Full-text PDF :	68
References:	37

Что такое QR-код?

Registration to the website

Logotypes