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

This article is cited in 5 scientific papers (total in 5 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:

Document Type: Article
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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  • https://doi.org/10.4213/im8169
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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  crossref  zmath  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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