Skip to main content
SpringerLink
Log in

Arithmetic Properties of Generalized Hypergeometric F-Series

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

Abstract

A generalization of the Siegel–Shidlovskii method in the theory of transcendental numbers is used to prove the infinite algebraic independence of elements (generated by generalized hypergeometric series) of direct products of fields \(\mathbb{K}_v\), which are completions of an algebraic number field \(\mathbb{K}\) of finite degree over the field of rational numbers with respect to valuations v of \(\mathbb{K}\) extending p-adic valuations of the field ℚ over all primes p, except for a finite number of them.

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

Similar content being viewed by others

References

  1. A. B. Shidlovskii, Transcendental Numbers (Nauka, Moscow, 1987; Walter de Gruyter, Berlin, 1989).

    Book  MATH  Google Scholar 

  2. V. Kh. Salikhov, Dokl. Akad. Nauk SSSR 307 (2), 284–286 (1989).

    Google Scholar 

  3. V. Kh. Salikhov, Acta Arithm. 53, 453–471 (1990).

    Article  Google Scholar 

  4. V. Kh. Salikhov, Math. USSR Sb. 69 (1), 203–226 (1991).

    Article  MathSciNet  Google Scholar 

  5. A. I. Galochkin, Math. USSR Sb. 24 (3), 385–407 (1974).

    Article  Google Scholar 

  6. G. V. Chudnovsky, Proc. Natl. Acad. Sci. USA 81, 7261–7265 (1985).

    Article  Google Scholar 

  7. E. Bombieri, “On G-functions,” Recent Progress in Analytic Number Theory (Academic, London, 1981), Vol. 2, pp. 1–68.

    MATH  Google Scholar 

  8. D. Bertrand, V. Chirskii, and J. Yebbou, Ann. Fac. Sci. Toulouse 13 (2), 241–260 (2004).

    Article  MathSciNet  Google Scholar 

  9. V. G. Chirskii, Izv. Math. 78 (6), 1244–1260 (2014).

    Article  MathSciNet  Google Scholar 

  10. V. G. Chirskii, Dokl. Math. 90 (3), 766–768 (2014).

    Article  MathSciNet  Google Scholar 

  11. V. G. Chirskii, Izv. Math. 81 (2), 444–461 (2017).

    Article  MathSciNet  Google Scholar 

  12. Yu. V. Nesterenko, Math. Notes. 5 (5), 352–358 (1969).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119992, Russia

    V. G. Chirskii

Authors
  1. V. G. Chirskii
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. G. Chirskii.

Additional information

Original Russian Text © V.G. Chirskii, 2018, published in Doklady Akademii Nauk, 2018, Vol. 483, No. 3.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chirskii, V.G. Arithmetic Properties of Generalized Hypergeometric F-Series. Dokl. Math. 98, 589–591 (2018). https://doi.org/10.1134/S106456241807013X

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S106456241807013X

Search

Navigation