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Matematicheskie Zametki, 2002, Volume 71, Issue 5, Pages 662–676
DOI: https://doi.org/10.4213/mzm375
(Mi mzm375)
 

This article is cited in 15 scientific papers (total in 15 papers)

Integrality of Power Expansions Related to Hypergeometric Series

W. V. Zudilin

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
References:
Abstract: In the present paper, we study the arithmetic properties of power expansions related to generalized hypergeometric differential equations and series. Defining the series $f(z),g(z)$ in powers of $z$ so that $f(z)$ and $f(z)\log z+g(z)$ satisfy a hypergeometric equation under a special choice of parameters, we prove that the series $q(z)=ze^{g(Cz)/f(Cz)}$ in powers of $z$ and its inversion $z(q)$ in powers of $q$ have integer coefficients (here the constant $C$ depends on the parameters of the hypergeometric equation). The existence of an integral expansion $z(q)$ for differential equations of second and third order is a classical result; for orders higher than 3 some partial results were recently established by Lian and Yau. In our proof we generalize the scheme of their arguments by using Dwork's $p$-adic technique.
Received: 31.10.2000
English version:
Mathematical Notes, 2002, Volume 71, Issue 5, Pages 604–616
DOI: https://doi.org/10.1023/A:1015827602930
Bibliographic databases:
Document Type: Article
UDC: 511.21+517.588
Language: Russian
Citation: W. V. Zudilin, “Integrality of Power Expansions Related to Hypergeometric Series”, Mat. Zametki, 71:5 (2002), 662–676; Math. Notes, 71:5 (2002), 604–616
Citation in format AMSBIB
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\paper Integrality of Power Expansions Related to Hypergeometric Series
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\yr 2002
\vol 71
\issue 5
\pages 662--676
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\transl
\jour Math. Notes
\yr 2002
\vol 71
\issue 5
\pages 604--616
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  • https://doi.org/10.4213/mzm375
  • https://www.mathnet.ru/eng/mzm/v71/i5/p662
  • This publication is cited in the following 15 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические заметки Mathematical Notes
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