Skip to main content
SpringerLink
Log in

Infinite Algebraic Independence of Some Almost Polyadic Numbers

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

Abstract

In this paper, we discuss some problems of infinite algebraic independence of polyadic and almost polyadic numbers.

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. D. Bertrand, V. Chirskii, and J. Yebbou, “Effective estimates for global relations on Euler-type series,” Ann. Fac. Sci. Toulouse, 13, No. 2, 241–260 (2004).

    Article  MathSciNet  MATH  Google Scholar 

  2. V. G. Chirskii, “On series that are algebraically independent in all local fields,” Vestn. Mosk. Univ. Ser. 1. Mat. Mekh., No. 3, 29–34 (1978).

  3. V. G. Chirskii, “On global relations,” Mat. Zametki, 48, No. 2, 123–127 (1990).

    MathSciNet  Google Scholar 

  4. V. G. Chirskii, “On algebraic relations in non-Archimedean fields,” Funkts. Anal. Prilozh., 26, No. 2, 41–50 (1992).

    MathSciNet  MATH  Google Scholar 

  5. V. G. Chirskii, “Siegel method in the p-adic domain,” Fundam. Prikl. Mat., 11, No. 6, 221–230 (2005).

    Google Scholar 

  6. V. G. Chirskii, “Generalization of the notion of a global relation,” Zap. Nauch. Semin. POMI, 322, 220–238 (2005).

    MATH  Google Scholar 

  7. V. G. Chirskii, “Arithmetic properties of polyadic series with periodic coefficients,” Doll. Ross. Akad. Nauk, 459, No. 6, 677–679 (2014).

    MathSciNet  MATH  Google Scholar 

  8. V. G. Chirskii, “On arithmetic properties of generalized hypergeometric series with irrational parameters,” Izv. Ross. Akad. Nauk. Ser. Mat., 78, No. 6, 193–210 (2014).

    MathSciNet  MATH  Google Scholar 

  9. V. G. Chirskii, “Arithmetic properties of integer polyadic numbers,” Chebyshev. Sb., 16, No. 1, 254–264 (2015).

    MathSciNet  MATH  Google Scholar 

  10. V. G. Chirskii, “Arithmetic properties of Euler series,” Vestn. Mosk. Univ. Ser. 1. Mat. Mekh., No. 1, 59–61 (2015).

  11. V. G. Chirskii, “Arithmetic properties of polyadic series with periodic coefficients,” Izv. Ross. Akad. Nauk. Ser. Mat., 81, No. 2, 215–232 (2017).

    MathSciNet  MATH  Google Scholar 

  12. V. G. Chirskii, “Topical problems of the theory of transcendental numbers: Developments of approaches to tyeir solutions in works of Yu. V. Nesterenko,” Russ. J. Math. Phys., 24, No. 2, 153–171 (2017).

    Article  MathSciNet  MATH  Google Scholar 

  13. V. G. Chirskii, “Arithmetic properties of generalized hypergeometric F-series,” Dokl. Ross. Akad. Nauk, 483, No. 3, 252–254 (2018).

    MathSciNet  MATH  Google Scholar 

  14. V. G. Chirskii and V. Yu. Matveev, “On a representation of natural numbers,” Chebyshev. Sb., 14, No. 1, 75–86 (2013).

    MATH  Google Scholar 

  15. V. G. Chirskii and V. Yu. Matveev, “On some properties of polyadic decompositions,” Chebyshev. Sb., 14, No. 2 (46), 164–172 (2013).

  16. A. A. Fomin, Number Rings and Modules over Them [in Russian], Prometey, Moscow (2013).

    Google Scholar 

  17. V. Yu. Matveev, “Algebraic independence of some almost polyadic series,” Chebyshev. Sb., 17, No. 3, 166–177 (2016).

    MathSciNet  MATH  Google Scholar 

  18. V. Yu. Matveev and V. G. Chirskii, “On some properties of polyadic expansions,” Chebyshev. Sb., 14, No. 2, 164–172 (2013).

    MATH  Google Scholar 

  19. A. G. Postnikov, Introduction to Analytic Number Theory [in Russian], Nauka, Moscow (1971).

    MATH  Google Scholar 

  20. V. Kh. Salikhov, “On the algebraic independence of values of the E-function satisfying first-order linear differential equations,” Mat. Zametki, 13, No. 1, 29–40 (1973).

    MathSciNet  Google Scholar 

  21. A. B. Shidlovskii, Transcendent Numbers [in Russian], Nauka, Moscow (1987).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Moscow State Pedagogical University, Moscow, Russia

    V. Yu. Matveev

Authors
  1. V. Yu. Matveev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. Yu. Matveev.

Additional information

Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 179, Proceedings of the International Conference “Classical and Modern Geometry” Dedicated to the 100th Anniversary of Professor Vyacheslav Timofeevich Bazylev. Moscow, April 22-25, 2019. Part 1, 2020.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Matveev, V.Y. Infinite Algebraic Independence of Some Almost Polyadic Numbers. J Math Sci 276, 379–383 (2023). https://doi.org/10.1007/s10958-023-06752-z

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-023-06752-z

Keywords and phrases

AMS Subject Classification

Search

Navigation