Skip to main content
SpringerLink
Log in

Algebraic independence of values of elliptic functions

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Brownawell, W.D.: The algebraic independence of certain values of the exponential function. K. norske Vidensk. Selsk. Skr. No. 23 (1972)

  2. Brownawell, W.D.: The algebraic independence of certain numbers related by the exponential function. J. Number Theory6, 22–31 (1974)

    Google Scholar 

  3. Brownawell, W.D., Kubota, K.K.: The algebraic independence of Weierstrass functions and some related numbers. Acta Arith.33, 111–149 (1971)

    Google Scholar 

  4. Brownawell, W.D., Masser, D.W.: Multiplicity estimates for analytic functions I. J. reine angew. Math.314, 200–216 (1980)

    Google Scholar 

  5. Chudnovsky, G.V.: Contributions to the theory of transcendental numbers. A.M.S. Surveys and Monographs, No. 19, 1984

  6. Gelfond, A.O.: Transcendental and algebraic numbers. New York: Dover 1960

    Google Scholar 

  7. Masser, D.W., Wüstholz, G.: Algebraic independence properties of values of elliptic functions. Journées Arithmétiques 1980, London Math. Soc. Lecture Notes Vol. 56 (ed. J.V. Armitage), Cambridge 1982

  8. Masser, D.W., Wüstholz, G.: Zero estimates on group varieties I. Invent. Math.64, 489–516 (1981)

    Google Scholar 

  9. Masser, D.W., Wüstholz, G.: Zero estimates on group varieties II. Invent. Math.80, 233–276 (1985)

    Google Scholar 

  10. Smelev, A.A.: On the method of A.O. Gelfond in the theory of transcendental numbers. Mat. Zametki10, 415–426 (1971); Math. Notes10, 672–678 (1971)

    Google Scholar 

  11. Smelev, A.A.: Algebraic independence of values of exponential and elliptic functions. Mat. Zametki20, 195–202 (1976); Math. Notes20, 669–673 (1976)

    Google Scholar 

  12. Smelev, A.A.: Algebraic independence of several numbers connected with exponential and elliptic functions. Ukr. Mat. Z.33, 277–282 (1981); Ukr. Math. J.33, 216–220 (1981)

    Google Scholar 

  13. Tijdeman, R.: On the number of zeroes of general exponential polynomials. Indagationes Math.33, 1–7 (1971)

    Google Scholar 

  14. Tijdeman, R.: On the algebraic independence of certain numbers. Indagationes Math.33, 146–162 (1971)

    Google Scholar 

  15. Waldschmidt, M.: Indépendance algébrique des valeurs de la fonction exponentielle. Bull. Soc. Math. Fr.99, 285–304 (1971)

    Google Scholar 

  16. Waldschmidt, M.: Solution du huitième problème de Schneider. J. Number Theory5, 191–202 (1973)

    Google Scholar 

  17. Wüstholz, G.: Algebraische Unabhängigkeit von Werten von Funktionen, die gewissen Differentialgleichungen genügen. J. reine angew. Math.317, 102–119 (1980)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Michigan, 48109-1003, Ann Arbor, MI, USA

    D. W. Masser

  2. Max-Planck-Institut für Mathematik, Gottfried-Claren-Strasse 26, D-5300, Bonn 3, Germany

    G. Wüstholz

  3. Bergische Universität-Gesamthochschule, FB 7, Gauß-Strasse 20, D-5600, Wuppertal, Germany

    G. Wüstholz

Authors
  1. D. W. Masser
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. Wüstholz
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Masser, D.W., Wüstholz, G. Algebraic independence of values of elliptic functions. Math. Ann. 276, 1–17 (1986). https://doi.org/10.1007/BF01450920

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01450920

Keywords

Search

Navigation