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Izv. RAN. Ser. Mat., 2014, Volume 78, Issue 6, Pages 193–210 (Mi izv8169)  

This article is cited in 10 scientific papers (total in 10 papers)

On the arithmetic properties of generalized hypergeometric series with irrational parameters

V. G. Chirskii

M. V. Lomonosov Moscow State University

Abstract: We prove the existence of an infinite set of primes $p$ such that the generalized hypergeometric series with irrational parameters in a number field $\mathbb{K}$ is not equal to zero in the algebraic extension $\mathbb{K}_v$ of the field of $p$-adic numbers, where $v$ is an extension of the $p$-adic valuation to $\mathbb{K}$.

Keywords: generalized hypergeometric series, irrational numbers, $p$-adic numbers.

DOI: https://doi.org/10.4213/im8169

Full text: PDF file (569 kB)
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English version:
Izvestiya: Mathematics, 2014, 78:6, 1244–1260

Bibliographic databases:

UDC: 511.36
MSC: 11J13, 11J91, 33C20
Received: 26.09.2013
Revised: 19.03.2014

Citation: V. G. Chirskii, “On the arithmetic properties of generalized hypergeometric series with irrational parameters”, Izv. RAN. Ser. Mat., 78:6 (2014), 193–210; Izv. Math., 78:6 (2014), 1244–1260

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. Yu. Matveev, “Algebraicheskaya nezavisimost nekotorykh pochti poliadicheskikh ryadov”, Chebyshevskii sb., 17:3 (2016), 166–177  mathnet  elib
    2. V. G. Chirskii, “Periodicheskie i neperiodicheskie konechnye posledovatelnosti”, Chebyshevskii sb., 18:2 (2017), 275–278  mathnet  crossref  elib
    3. E. S. Krupitsyn, “Otsenka mnogochlena ot globalno transtsendentnogo poliadicheskogo chisla”, Chebyshevskii sb., 18:4 (2017), 256–260  mathnet  crossref  elib
    4. K. Vaananen, “On Padé approximations and global relations of some Euler-type series”, Int. J. Number Theory, 14:8 (2018), 2303–2315  crossref  mathscinet  zmath  isi  scopus
    5. V. G. Chirskii, “Arithmetic properties of generalized hypergeometric $F$-series”, Dokl. Math., 98:3 (2018), 589–591  mathnet  crossref  zmath  isi  elib
    6. V. Yu. Matveev, “Svoistva elementov pryamykh proizvedenii polei”, Chebyshevskii sb., 20:2 (2019), 383–390  mathnet  crossref
    7. E. S. Krupitsyn, “Arifmeticheskie svoistva ryadov nekotorykh klassov”, Chebyshevskii sb., 20:2 (2019), 374–382  mathnet  crossref
    8. V. Yu. Matveev, “Beskonechnaya algebraicheskaya nezavisimost nekotorykh pochti poliadicheskikh chisel”, Trudy mezhdunarodnoi konferentsii Klassicheskaya i sovremennaya geometriya, posvyaschennoi 100-letiyu so dnya rozhdeniyaprofessora Vyacheslava Timofeevicha Bazyleva. Moskva, 2225 aprelya 2019 g. Chast 1, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 179, VINITI RAN, M., 2020, 29–33  mathnet  crossref
    9. V. G. Chirskii, “Algebraicheskie svoistva tochek nekotorogo beskonechnomernogo metricheskogo prostranstva”, Trudy mezhdunarodnoi konferentsii Klassicheskaya i sovremennaya geometriya, posvyaschennoi 100-letiyu so dnya rozhdeniyaprofessora Vyacheslava Timofeevicha Bazyleva. Moskva, 2225 aprelya 2019 g. Chast 1, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 179, VINITI RAN, M., 2020, 81–87  mathnet  crossref
    10. 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 rozhdeniyaprofessora Vyacheslava Timofeevicha Bazyleva. Moskva, 2225 aprelya 2019 g. Chast 1, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 179, VINITI RAN, M., 2020, 88–93  mathnet  crossref
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