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Chebyshevskii Sbornik, 2021, Volume 22, Issue 2, Pages 519–527
DOI: https://doi.org/10.22405/2226-8383-2018-22-2-519-527
(Mi cheb1051)
 

This article is cited in 2 scientific papers (total in 2 papers)

BRIEF MESSAGE

Arithmetic properties of the values some hypergeometric F-series

A. Kh. Munos Vaskes

Moscow State Pedagogical University (Moscow)
Full-text PDF (662 kB) Citations (2)
References:
Abstract: Generalized hypergeometric series are of the form
f(z)=n=0(a1)n(al)n(b1)n(bm)nzn
If l<m and if the parameters are rational, they are closely related to Siegel's E-functions. If l=m and if the parameters are rational, they are G-functions. For l>m and if the parameters are rational, they are F-series.
The arithmetic properties values of generalized hypergeometric series is an actual problem with a long history. We shall only mention Siegel C. L., Shidlovskii A. B., Salikhov V. Kh., Beukers F., Brownawell W. D., Heckman G., Galochkin A. I., Oleinikov V. A., Ivankov P. L., Gorelov V. A., Chirskii V. G., Zudilin W., Matala–Aho T. etc.
We consider the so–called F-series. Chirskii V.G. proved the infinitу algebraic independence of the corresponding values.
Here we obtain lower estimates of polynomials and linear forms in the values of these series and their derivatives in a concrete p-adic field.
Keywords: F-series, estimates linear forms and polynomials, p-adic numbers.
Document Type: Article
UDC: 511.36
Language: Russian
Citation: A. Kh. Munos Vaskes, “Arithmetic properties of the values some hypergeometric F-series”, Chebyshevskii Sb., 22:2 (2021), 519–527
Citation in format AMSBIB
\Bibitem{Mun21}
\by A.~Kh.~Munos Vaskes
\paper Arithmetic properties of the values some hypergeometric $F$-series
\jour Chebyshevskii Sb.
\yr 2021
\vol 22
\issue 2
\pages 519--527
\mathnet{http://mi.mathnet.ru/cheb1051}
\crossref{https://doi.org/10.22405/2226-8383-2018-22-2-519-527}
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  • https://www.mathnet.ru/eng/cheb1051
  • https://www.mathnet.ru/eng/cheb/v22/i2/p519
  • This publication is cited in the following 2 articles:
    1. V. G. Chirskii, “Polyadic Liouville numbers”, Doklady Mathematics (Supplementary issues), 106:2 (2022), 137–141  mathnet  crossref  crossref
    2. V. G. Chirskii, “On polyadic Liouville numbers”, Doklady Mathematics (Supplementary issues), 106:2 (2022), 161–164  mathnet  crossref  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    References:13
     
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