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Izv. RAN. Ser. Mat., 1996, Volume 60, Issue 1, Pages 87–114 (Mi izv63)  

This article is cited in 4 scientific papers (total in 4 papers)

On a measure of irrationality for values of $G$-functions

W. V. Zudilin

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: It is shown that values of $G$-functions satisfying a system of linear differential equations are irrational at rational points $a/b$ with $a\in\mathbb Z$ and $b\in\mathbb N$ such that $b>C(\varepsilon)|a|^{2+\varepsilon}$ for an arbitrary positive $\varepsilon$. In the case of a generalized polylogarithmic function
$$ f(z)=\sum_{\nu=1}^\infty\frac{z^\nu}{(\nu+\lambda)^m}, \quad m\geqslant 2, \enskip \lambda\in\mathbb Q\setminus\{-1,-2,…\}, $$
an explicit form of $C(\varepsilon)$ is found.

DOI: https://doi.org/10.4213/im63

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English version:
Izvestiya: Mathematics, 1996, 60:1, 91–118

Bibliographic databases:

UDC: 511.36
MSC: 11J82
Received: 07.07.1995

Citation: W. V. Zudilin, “On a measure of irrationality for values of $G$-functions”, Izv. RAN. Ser. Mat., 60:1 (1996), 87–114; Izv. Math., 60:1 (1996), 91–118

Citation in format AMSBIB
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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. W. V. Zudilin, “On the algebraic structure of functional matrices of special form”, Math. Notes, 60:6 (1996), 642–648  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. W. V. Zudilin, “Cancellation of factorials”, Sb. Math., 192:8 (2001), 1181–1207  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. E. A. Ulanskii, “Identities for Generalized Polylogarithms”, Math. Notes, 73:4 (2003), 571–581  mathnet  crossref  crossref  mathscinet  zmath  isi
    4. Fischler S., Rivoal T., “Rational Approximation to Values of G-Functions, and Their Expansions in Integer Bases”, Manuscr. Math., 155:3-4 (2018), 579–595  crossref  mathscinet  zmath  isi  scopus  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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