Skip to main content
Log in

Somos-4 and elliptic systems of sequences

  • Mathematics
  • Published:
Doklady Mathematics Aims and scope Submit manuscript

Abstract

A general formula for elements of double Somos-4 sequences is obtained. A sufficient integrality condition for such sequences is presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. N. I. Akhiezer, Elements of the Theory of Elliptic Functions (Am. Math. Soc., Providence, RI, 1990; Nauka, Moscow, 1970).

    Google Scholar 

  2. E. T. Whittaker and G. N. Watson, A Course of Modern Analysis (Cambridge Univ. Press, Cambridge, 1952; Fizmatgiz, Moscow, 1963), Vol. 2.

    MATH  Google Scholar 

  3. G. Bastien and M. Rogalski, J. Math. Anal. Appl. 300, 303–333 (2004).

    Article  Google Scholar 

  4. S. Fomin and A. Zelevinsky, Adv. Appl. Math. 28, 119–144 (2002).

    Article  Google Scholar 

  5. A. Hone, Bull. London Math. Soc. 37, 161–171 (2005).

    Article  MathSciNet  Google Scholar 

  6. A. Hone, Trans. Am. Math. Soc. 359, 5019–5034 (2007).

    Article  Google Scholar 

  7. A. N. Hone and C. Swart, Math. Proc. Cambidge Philos. Soc. 145, 65–85 (2008).

    Google Scholar 

  8. A. Iatrou and J. A. G. Roberts, J. Phys. A: Math. Gen. 34, 6617–6636 (2001).

    Article  Google Scholar 

  9. A. Iatrou and J. A. G. Roberts, Nonlinearity 15, 459–489 (2002).

    Article  MathSciNet  Google Scholar 

  10. X. Ma, Discrete Math. 310, 1–5 (2010).

    Article  MathSciNet  Google Scholar 

  11. G. Quispel, J. Roberts, and C. Thompson, Physica D: Nonlinear Phenomena 34, 183–192 (1989).

    Article  Google Scholar 

  12. R. Shipsey, Elliptic Divisibility Sequences, PhD Thesis (Univ. of London, London, 2000).

    Google Scholar 

  13. C. S. Swart, Elliptic Curves and Related Sequences, PhD Thesis (Royal Holloway, Univ. of London, London, 2003).

    Google Scholar 

  14. T. Tsuda, J. Phys. A: Math. Gen. 37, 2721–2730 (2004).

    Article  Google Scholar 

  15. M. Ward, Am. J. Math. 70, 31–74 (1948).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to V. A. Bykovskii.

Additional information

Original Russian Text © V.A. Bykovskii, A.V. Ustinov, 2016, published in Doklady Akademii Nauk, 2016, Vol. 471, No. 1, pp. 7–10.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bykovskii, V.A., Ustinov, A.V. Somos-4 and elliptic systems of sequences. Dokl. Math. 94, 611–614 (2016). https://doi.org/10.1134/S1064562416060016

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1064562416060016

Navigation