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Russian Mathematical Surveys, 2011, Volume 66, Issue 2, Pages 369–420
DOI: https://doi.org/10.1070/RM2011v066n02ABEH004742 (Mi rm9420) 		 
This article is cited in 18 scientific papers (total in 18 papers)

Arithmetic hypergeometric series

W. Zudilin

School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, Australia
English version PDF (939 kB) Citations (18)
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DOI: https://doi.org/10.1070/RM2011v066n02ABEH004742
Abstract: The main goal of this survey is to give common characteristics of auxiliary hypergeometric functions (and their generalisations), functions which occur in number-theoretic problems. Originally designed as a tool for solving these problems, the hypergeometric series have become a connecting link between different areas of number theory and mathematics in general.
Bibliography: 183 titles.
Keywords: hypergeometric series, zeta value, Ramanujan's mathematics, Diophantine approximation, irrationality measure, modular form, Calabi–Yau differential equation, Mahler measure, Wilf–Zeilberger theory, algorithm of creative telescoping.
Received: 18.02.2011
Russian version:
Uspekhi Matematicheskikh Nauk, 2011, Volume 66, Issue 2(398), Pages 163–216
DOI: https://doi.org/10.4213/rm9420
Bibliographic databases:
Document Type: Article
UDC: 511+517
MSC: Primary 33C20; Secondary 05A19, 11B65, 11F11, 11J82, 11M06, 11Y60, 14H52
Language: English
Original paper language: Russian
Citation: W. Zudilin, “Arithmetic hypergeometric series”, Russian Math. Surveys, 66:2 (2011), 369–420
Citation in format AMSBIB
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\paper Arithmetic hypergeometric series
\jour Russian Math. Surveys
\yr 2011
\vol 66
\issue 2
\pages 369--420
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  • https://www.mathnet.ru/eng/rm/v66/i2/p163
    • This publication is cited in the following 18 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:1161
    Russian version PDF:566
    English version PDF:32
    References:110
    First page:50
     
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