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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)
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.
Citation:
A. Kh. Munos Vaskes, “Arithmetic properties of the values some hypergeometric F-series”, Chebyshevskii Sb., 22:2 (2021), 519–527
Linking options:
https://www.mathnet.ru/eng/cheb1051 https://www.mathnet.ru/eng/cheb/v22/i2/p519
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