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 Kv, which are completions of an algebraic number field K of finite degree over the field of rational numbers with respect to valuations v of K extending p-adic valuations of the field Q over all primes p, except for a finite number of them.
This publication is cited in the following 15 articles:
V. G. Chirskii, “Infinite linear independence with constraints on a subset of prime numbers of values of Eulerian-type series with polyadic Liouville parameter”, Doklady Mathematics (Supplementary issues), 106:2 (2022), 154–160
A. S. Samsonov, “Arifmeticheskie svoistva elementov pryamykh proizvedenii p-adicheskikh polei, II”, Chebyshevskii sb., 22:2 (2021), 236–256
V. G. Chirskii, “Arithmetic properties of values at polyadic Liouville points of Euler-type series with polyadic Liouville parameter”, Doklady Mathematics (Supplementary issues), 106:2 (2022), 150–153
E. Yu. Yudenkova, “Beskonechnaya lineinaya i algebraicheskaya nezavisimost znachenii F-ryadov v poliadicheskikh liuvillevykh tochkakh”, Chebyshevskii sb., 22:2 (2021), 334–346
A. S. Samsonov, “Ob odnom primenenii metodov issledovaniya algebraicheskoi nezavisimosti gipergeometricheskikh ryadov i znachenii g-adicheskikh funktsii”, Chebyshevskii sb., 22:2 (2021), 528–535
E. Yu. Yudenkova, “Znacheniya gipergeometricheskikh F-ryadov v poliadicheskikh liuvillevykh tochkakh”, Chebyshevskii sb., 22:2 (2021), 536–542
V. Yu. Matveev, “Beskonechnaya algebraicheskaya nezavisimost nekotorykh pochti poliadicheskikh chisel”, Trudy mezhdunarodnoi konferentsii «Klassicheskaya i sovremennaya geometriya»,
posvyaschennoi 100-letiyu so dnya rozhdeniya professora Vyacheslava Timofeevicha Bazyleva.
Moskva, 22–25 aprelya 2019 g. Chast 1, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 179, VINITI RAN, M., 2020, 29–33
V. G. Chirskii, “Algebraicheskie svoistva tochek nekotorogo beskonechnomernogo metricheskogo prostranstva”, Trudy mezhdunarodnoi konferentsii «Klassicheskaya i sovremennaya geometriya»,
posvyaschennoi 100-letiyu so dnya rozhdeniya professora Vyacheslava Timofeevicha Bazyleva.
Moskva, 22–25 aprelya 2019 g. Chast 1, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 179, VINITI RAN, M., 2020, 81–87
E. Yu. Yudenkova, “Beskonechnaya lineinaya nezavisimost znachenii obobschennykh gipergeometricheskikh ryadov s irratsionalnymi parametrami v poliadicheskikh tochkakh”, Trudy mezhdunarodnoi konferentsii «Klassicheskaya i sovremennaya geometriya»,
posvyaschennoi 100-letiyu so dnya rozhdeniya professora Vyacheslava Timofeevicha Bazyleva.
Moskva, 22–25 aprelya 2019 g. Chast 1, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 179, VINITI RAN, M., 2020, 88–93
A. Kh. Munos Vaskes, “Otsenki snizu mnogochlenov i lineinykh form ot znachenii F-ryadov”, Chebyshevskii sb., 21:3 (2020), 142–164
A. S. Samsonov, “Arifmeticheskie svoistva elementov pryamykh proizvedenii p-adicheskikh polei”, Chebyshevskii sb., 21:4 (2020), 227–242
V. Yu. Matveev, “Svoistva elementov pryamykh proizvedenii polei”, Chebyshevskii sb., 20:2 (2019), 383–390
E. S. Krupitsyn, “Arifmeticheskie svoistva ryadov nekotorykh klassov”, Chebyshevskii sb., 20:2 (2019), 374–382
V. G. Chirskii, “Product Formula, Global Relations, and Polyadic Numbers”, Russ. J. Math. Phys., 26:3 (2019), 286
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