Abstract
In this paper, we report on the development of the theory of transcendental numbers in a polyadic domain, which is an infinite-dimensional metric space, namely, the direct product of fields of p-adic numbers.
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References
Y. André, G-Functions and Geometry, Friedr. Vieweg, Wiesbaden (1989).
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).
E. Bombieri, “On G-functions,” in: Recent Progress in Analytic Number Theory, Academic Press, London (1981), pp. 1–68.
V. G. Chirskii, “Arithmetic properties of polyadic series with periodic coefficients,” Dokl. Ross. Akad. Nauk, 459, No. 6, 677–679 (2014).
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).
V. G. Chirskii, “Arithmetic properties of polyadic series with periodic coefficients,” Izv. Ross. Akad. Nauk. Ser. Mat., 81, No. 2, 215–232 (2017).
V. G. Chirskii, “Arithmetic properties of heneral hypergeometric F-series,” Dokl. Ross. Akad. Nauk, 483, No. 3, 252–254 (2018).
V. G. Chirskii and V. Yu. Matveev, “On a reprsentation of natural numbers,” Chebyshev. Sb., 14, No. 1, 75–86 (2013).
G. V. Chudnovskii, “On applications of Diophantine approximations,” Proc. Natl. Acad. Sci. U.S.A., 81, 7261–7265 (1985).
A. A. Fomin, Numerical Rings and Modules over Them [in Russian], Prometei, Moscow (2013).
A. I. Galochkin, “Lower estimate for polynomials of values of analytical functions,” Mat. Sb., 95 (137), No. 3 (11), 396–417 (1974).
V. Yu. Matveev, “Algebraic independence of some almost polyadic series,” Chebyshev. Sb., 17, No. 3, 156–167.
Yu. V. Nesterenko, “Hermite–Padé approximations of generalized hypergeometric functions,” Mat. Sb., 185, No. 3, 39–72 (1994).
E. V. Novoselov, “On integration on a bicompact ring and its applications to the number theory,” Izv. Vyssh. Ucheb. Zaved. Mat., 3 (22), 66–79 (1961).
A. G. Postnikov, Introduction to Analytic Number Theory [in Russian], Nauka, Moscow (1971).
V. Kh. Salikhov, “In algebraic independence of values of hypergeometric E-functions,” Dokl. Akad. Nauk SSSR, 307, No. 2, 284–286 (1989).
V. Kh. Salikhov, “Irreducibility of hypergeometric equations and algebraic independence of values of E-functions,” Acta Arithm., 53, 453–471 (1990).
V. Kh. Salikhov, “Criterion of algebraic independence of values of one class of hypergeometric E-functions,” Mat. Sb., 181, No. 2, 189–211 (1990).
A. B. Shidlovskii, Transcendental Numbers [in Russian], Nauka, Moscow (1987).
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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 V. T. Bazylev. Moscow, April 22-25, 2019. Part 1, 2020.
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Chirskii, V.G. Algebraic Properties of Points of Some Infinite-Dimensional Metric Spaces. J Math Sci 276, 430–436 (2023). https://doi.org/10.1007/s10958-023-06761-y
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DOI: https://doi.org/10.1007/s10958-023-06761-y