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A review of the results on polyadic Liouville numbers

https://doi.org/10.22405/2226-8383-2025-26-4-316-328

Abstract

The paper presents a lover estimate for the 𝑝-adic value of a polynomial evaluated at polyadic Liouville number.

About the Author

Evgeny Stanislavovich Krupitsyn
Institute of Mathematics and Computer Science, Moscow Pedagogical State University
Russian Federation

candidate of physical and mathematical sciences



References

1. Waldschmidt M. 1974, “Nombres Transcendants”, Lecture Notes in Mathematics 402. Springer. pp. 181–192.

2. Waldschmidt M. 1984, “Algebraic independence of transcendental numbers. Gelfond’s method and its developments”, Prespectives in Mathematics. Birkh¨auser Basel Boston. pp. 551–557.

3. Postnikov A.G. 1971, Introduction to the analytical theory of numbers. Moscow: Nauka.

4. Pontryagin L.S. 1984, Continuous groups. Moscow: Nauka.

5. Kurepa D. 1971, “On the left factorial function !𝑛”, Mathematica Balkanica 1. pp. 147–153.

6. Chirskii V.G. and Matveev V.Yu. 2013, “On representations of natural numbers”, Chebyshevskii Sbornik 14(1). pp. 75–86.

7. Chirskii V.G. 2020, “Arithmetic properties of generalized hypergeometric series”, Russian Journal of Mathematical Physics 27(2). pp. 175–184.

8. Chirskii V.G. 2019, “Product formula global relations and polyadic integers”, Russian Journal of Mathematical Physics 26(3). pp. 286–305.

9. Chirskii V.G. 2024, “Infinite algebraic independence of polyadic series with periodic coefficients”, Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya 519(6). pp. 16–19.

10. Chirskii V.G. 2021, “Polyadic Liouville numbers”, Chebyshevskii Sbornik 22(3). pp. 245–255.

11. Chirskii V.G. 2014, “On the arithmetic properties of generalized hypergeometric series with irrational parameters”, Izvestiya Rossiiskoi Akademii Nauk 78(6). pp. 193–210.

12. Chudnovsky G.V. 1985, “On applications of Diophantine approximations”, Proceedings of the National Academy of Sciences of the United States of America 81. pp. 7261–7265.

13. Chirskii V.G. 2021, “On polyadic Liouville numbers”, Chebyshevskii Sbornik 22(5). pp. 243–251.

14. Krupitsyn E.S. 2019, “Arithmetic properties of series of some classes”, Chebyshevskii Sbornik 20(2). pp. 374–382.

15. Krupitsyn E.S. 2017, “Estimates of polynomials in a Liouvillean polyadic integer”, Chebyshevskii Sbornik 18(4). pp. 255–259.

16. Erd˝os P. 1962, “Representation of real numbers as sums and product of Liouville numbers”, Michigan Mathematical Journal 9(1). pp. 59–60.

17. Galochkin A.I. 1970, “On the algebraic independence of the values of 𝐸-functions in some transcendental points”, Bulletin of Moscow State University. Series 1: Mathematics Mechanics 5. pp. 58–63.

18. Shidlovsky A.B. 1987, Transcendental numbers. Moscow: Nauka.

19. Chirskii V.G. 2019, “Product formula global relations and polyadic integers”, Russian Journal of Mathematical Physics 26(3). pp. 286–305.

20. Chirskii V.G. 2022, “New problems in the theory of transcendental polyadic numbers”, Doklady Mathematics 106(1). pp. 265–267.

21. Chirskii V.G. 2022, “Arithmetic properties of the values of generalized hypergeometric series with polyadic transcendental parameters”, Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya 506. pp. 95–107.

22. Chirskii V.G. 2020, “Arithmetic properties of Eulerian type series with parameter — Liouville polyadic number”, Doklady Mathematics 494. pp. 65–67.

23. Chirskii V.G. 2023, “Transcendence of 𝑝-adic values of generalized hypergeometric series with transcendental polyadic parameters”, Doklady Mathematics 510. pp. 29–32.

24. Chirskii V.G. 2023, “The transcendence of some 2-adic numbers”, Chebyshevskii Sbornik 24(5). pp. 194–200.


Review

For citations:


Krupitsyn E.S. A review of the results on polyadic Liouville numbers. Chebyshevskii Sbornik. 2025;26(4):316-328. (In Russ.) https://doi.org/10.22405/2226-8383-2025-26-4-316-328

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