Russian Mathematical Surveys
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Uspekhi Mat. Nauk:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

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)
References:
PDF
HTML
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”, Uspekhi Mat. Nauk, 66:2(398) (2011), 163–216; Russian Math. Surveys, 66:2 (2011), 369–420
Citation in format AMSBIB
\Bibitem{Zud11}
\by W.~Zudilin
\paper Arithmetic hypergeometric series
\jour Uspekhi Mat. Nauk
\yr 2011
\vol 66
\issue 2(398)
\pages 163--216
\mathnet{http://mi.mathnet.ru/rm9420}
\crossref{https://doi.org/10.4213/rm9420}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2847791}
\zmath{https://zbmath.org/?q=an:1225.33008}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2011RuMaS..66..369Z}
\elib{https://elibrary.ru/item.asp?id=20423184}
\transl
\jour Russian Math. Surveys
\yr 2011
\vol 66
\issue 2
\pages 369--420
\crossref{https://doi.org/10.1070/RM2011v066n02ABEH004742}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000294606300004}
\elib{https://elibrary.ru/item.asp?id=17156152}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79960160945}
Linking options:
  • https://www.mathnet.ru/eng/rm9420
  • https://doi.org/10.1070/RM2011v066n02ABEH004742
  • 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
    Related articles in Google Scholar: Russian articles, English articles
    		Успехи математических наук Russian Mathematical Surveys
    Statistics & downloads:
    Abstract page:1148
    Russian version PDF:557
    English version PDF:30
    References:108
    First page:50
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024