Skip to main content
Log in

Certain arithmetic properties of coefficients of Kummer’s function

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

We estimate the common denominators of the first n coefficients of Kummer’s function with parameters belonging to an arbitrary quadratic field.

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.

Similar content being viewed by others

References

  1. A. I. Galočkin, “The arithmetic properties of the values of some entire hypergeometric functions,” Sib. Mat. Zh., 17, No. 6, 1220–1235 (1976).

    Google Scholar 

  2. A. I. Galočkin, “Criterion for membership of hypergeometric Siegel functions in a class of E-functions,” Mat. Zametki, 29, No. 1, 3–14 (1981).

    MathSciNet  Google Scholar 

  3. A. B. Shidlovskii, Transcendental Numbers, Studies in Math., Vol. 12, Walter de Gruyter, Berlin (1989).

    Google Scholar 

  4. C. L. Siegel, “Über einige Anwendungen Diophantischer Approximationen,” Abh. Preuss. Akad. Wiss., Phys.-Math. Kl., No. 1, 1–70 (1929).

  5. C. L. Siegel, Transcendental Numbers, Princeton University Press, Princeton (1949).

    MATH  Google Scholar 

  6. V. G. Sprindžuk, “Irrationality of the values of certain transcendental functions,” Izv. Akad. Nauk SSSR, Ser. Mat., 32, No. 1, 93–107 (1968).

    MathSciNet  Google Scholar 

  7. V. G. Sprindžuk, “On the theory of Siegel’s hypergeometric functions,” Dokl. Akad. Nauk BSSR, 13, No. 5, 389–391 (1969).

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. I. Galochkin.

Additional information

__________

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 6, pp. 27–32, 2005.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Galochkin, A.I. Certain arithmetic properties of coefficients of Kummer’s function. J Math Sci 146, 5644–5648 (2007). https://doi.org/10.1007/s10958-007-0379-8

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-007-0379-8

Keywords

Navigation