Estimates of linear forms in values of generalized hypergeometric series with polyadic transcendental parameters
https://doi.org/10.22405/2226-8383-2025-26-4-419-431
Abstract
Theorems are proved concerning estimates of linear forms in values of generalized hypergeometric series of the form Σ︀∞ 𝑛=0 (𝛼1)𝑛 . . . (𝛼𝑚−1)𝑛 𝑧𝑛, among the parameters of which are transcendental 𝑝-adic Liouville numbers
About the Author
Ekaterina Yurjevna YudenkovaRussian Federation
References
1. Chirskii, V. G. 2022, “Arithmetic properties of values of generalized hypergeometric series with polyadic transcendental parameters”, Reports of the Russian Academy of Sciences, vol.506.pp.95-107. DOI:10.31857/S2686954322050071.
2. Chirskii, V. G. 2022, “New problems in the theory of transcendental polyadic numbers”, Reports of the Russian Academy of Sciences, vol.505, pp.63-65. DOI:10.31857/S2686954322040075.
3. Chirskii, V. G. 2020, “Arithmetic properties of Euler-type series with polyadic Liouville parameter”, Reports of the Russian Academy of Sciences, vol.494, pp.69-70. DOI:10.31857/S268695432005032X.
4. Chirskii, V. G. 2021, “Arithmetic Properties of an Euler-Type Series with Polyadic Liouvillean Parameter”, Russ.J.Math.Phys., vol.28, pp.294-302. DOI:10.1134/S1061920819030051.
5. Chirskii, V. G. 2022, “Polyadic Estimates for F-Series”, Doklady Mathematics, vol.106, pp.134-136.
6. Chirskii, V. G. 2022, “Estimates of Linear Forms and Polinomials in Polyadic Numbers”, Doklady Mathematics, vol.106, pp.131-133.
7. Chirskii, V. G. 2022, “Arithmetic Properties of Values at Polyadic Liouville Point of Euler-Type Series with Polyadic Liouville Parameter”, Doklady Mathematics, vol.106, pp.150-153.
8. Chirskii, V. G. 2021, “Arithmetic properties of values at polyadic Liouville points of series with a polyadic Liouville parameter”, Chebyshevskiy Sbornik, vol.22, pp.156-167. DOI:10.22405/2226-8383-2021-22-2-304-312
9. Nesterenko, Yu.V. 1994, “Hermite-Pad´e approximations of generalized hypergeometric functions”, Mathematical Collection, vol.185, pp.39-72.
10. Postnikov, A. G. 1971, “Introduction to Analytic Number Theory”, Nauka, pp.416.
11. Ernvall-Hytonen, A-M., Matala-aho, T., Seppela, L. 2019, “Euler’s divergent series in arithmetic progressions”, J.Integer Sequences, V.22, Article 19.2.2, p.10.
12. Matala-aho, T., Zudilin, W. 2018, “Euler factorial series and global relations”, J. Number Theory, vol.186, pp.202-210. DOI:10.1016/j.jnt.2017.09.026
13. Shidlovskiy, A. B. 1987, “Transcendental number”, Nauka, pp.448.
14. Salikhov, V. H. 1990, “A criterion for algebraic independence of one class of hypergeometric 𝐸-functions”, Mathematical Collection, vol.181, pp.189-211.
15. Salikhov, V. H. 1990, “Irreducibility of hypergeometric equations and algebraic independence of values of 𝐸-functions ”, Acta Arithm, vol.53, pp.453-471.
16. Bombieri, E. 1990, “𝐺-functions”, Recent Progress in Analytic Number Theory, London: Academic Press, vol.2, pp.1-68.
17. Galochkin, A. I. 1970, “On the algebraic independence of values of 𝐸 -functions at certain transcendental points”, Vestnik Moskovskogo universiteta, vol.5, pp.58-63.
18. Bertrand, D., Chiskii, V., Yebbou, J. 2004, “Effective estimates for global relations on Euler-type series”, Ann. Fac. Sci. Toulouse, vol.13, num.2, pp.241-260.
19. Chirskii, V. G. 2019, “Product Formula, Global Relations and Polyadic Integers”, Russ. J. Math. Phys., vol.26, pp.286-305. DOI:10.1134/S1061920821030031
20. Chirskii, V. G. 2014, “On the arithmetic properties of generalized hypergeometric series with irrational parameters”, Izvestiya Russian Academy of Sciences, vol.78, num.6, pp.286-305. DOI: https://doi.org/10.4213/im8169
21. Prakhar, K. 1967, “Distribution of Prime Numbers”, Mir.
Review
For citations:
Yudenkova E.Yu. Estimates of linear forms in values of generalized hypergeometric series with polyadic transcendental parameters. Chebyshevskii Sbornik. 2025;26(4):419-431. (In Russ.) https://doi.org/10.22405/2226-8383-2025-26-4-419-431






















