Skip to main content
Log in

On transcendence and algebraic independence of the values of Kummer's functions

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

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.

Literature Cited

  1. C. Siegel, “Uber einige Anwendungen Diophantische Approximation,” Abh. Preuss. Acad. Wiss., No. 1, 1–70 (1929–1930).

    Google Scholar 

  2. C. Siegel, Transcendental Numbers, Annals of Math. Studies No. 16, Princeton University Press, Princeton (1949).

    Google Scholar 

  3. A. O. Gel'fond, Transcendental and Algebraic Numbers [Russian translation], Dover, New York (1960).

    Google Scholar 

  4. A. B. Shidlovskii, “On criteria for the algebraic independence of the values of a class of entire functions,” Izv. Akad. Nauk SSSR, Ser. Mat.,23, No. 1, 35–66 (1959).

    Google Scholar 

  5. A. B. Shidlovskii, “On the transcendence and algebraic independence of the values of E-functions associated with an arbitrary number of algebraic equations in the field of rational functions,” Izv. Akad. Nauk SSSR, Ser. Mat.,26, No. 6, 877–910 (1962).

    Google Scholar 

  6. S. Lang, “A transcendence measure for E-functions,” Math.,9, 157–161 (1962).

    Google Scholar 

  7. A. B. Shidlovskii, “On bounds for the measure of transcendence of the values of E-functions,” Matem. Zametki,2, No. 1, 33–44 (1967).

    Google Scholar 

  8. A. B. Shidlovskii, “On transcendence and algebraic independence of entire functions of certain classes,” Dokl. Akad. Nauk SSSR,96, No. 4, 697–700 (1954); Uch. Zap. MGU, Matem., No. 186,9, 11–70 (1952).

    Google Scholar 

  9. A. B. Shidlovskii, “On the algebraic independence of a class of transcendental numbers,” Dokl. Akad. Nauk SSSR,108, No. 3, 400–403 (1956); “On the transcendence and algebraic independence of the values of certain functions,” Trudy Mosk. Matem. Ob-va,8, 283–320 (1959).

    Google Scholar 

  10. A. B. Shidlovskii, “On the transcendence and algebraic independence of the values of certain E-functions,” Vestn. Mosk. Gos. Un-ta, Ser. 1, No. 5, 44–59 (1961).

    Google Scholar 

  11. A. B. Shidlovskii, “On the transcendence and algebraic independence of the values of E-functions satisfying linear nonhomogeneous differential equations of the second order,” Dokl. Akad. Nauk SSSR,169, No. 1, 42–45 (1966).

    Google Scholar 

  12. V. A. Oleinikov, “On the transcendence and algebraic independence of teh values of certain E-functions,” Vestn. Mosk. Gos. Un-ta, Ser. 1, No. 6, 34–38 (1962).

    Google Scholar 

Download references

Authors

Additional information

Translated from Sibirskii Matematicheskii Zhurnal, Vol. 12, No. 5, pp. 961–982, September–October, 1971.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Belogrivov, I.I. On transcendence and algebraic independence of the values of Kummer's functions. Sib Math J 12, 690–705 (1971). https://doi.org/10.1007/BF00966507

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00966507

Keywords

Navigation