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Uspekhi Mat. Nauk, 2011, Volume 66, Issue 2(398), Pages 163–216 (Mi umn9420)  

This article is cited in 10 scientific papers (total in 10 papers)

Arithmetic hypergeometric series

W. Zudilin

School of Mathematical and Physical Sciences, University of Newcastle, Callaghan, Australia

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.

DOI: https://doi.org/10.4213/rm9420

Full text: PDF file (1044 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2011, 66:2, 369–420

Bibliographic databases:

UDC: 511+517
MSC: Primary 33C20; Secondary 05A19, 11B65, 11F11, 11J82, 11M06, 11Y60, 14H52
Received: 18.02.2011

Citation: W. Zudilin, “Arithmetic hypergeometric series”, Uspekhi Mat. Nauk, 66:2(398) (2011), 163–216; Russian Math. Surveys, 66:2 (2011), 369–420

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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. M. Zakrzewski, H. Żołądek, “Linear differential equations and multiple zeta-values. III. Zeta(3)”, J. Math. Phys., 53:1 (2012), 013507, 40 pp.  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. J. Guillera, “More hypergeometric identities related to Ramanujan-type series”, Ramanujan J., 32:1 (2013), 5–22  crossref  mathscinet  zmath  isi  scopus
    3. P. B. Slater, “A concise formula for generalized two-qubit Hilbert–Schmidt separability probabilities”, J. Phys. A, 46:44 (2013), 445302, 13 pp.  crossref  mathscinet  zmath  adsnasa  isi  scopus
    4. E. A. Rakhmanov, S. P. Suetin, “The distribution of the zeros of the Hermite-Padé polynomials for a pair of functions forming a Nikishin system”, Sb. Math., 204:9 (2013), 1347–1390  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. M. A. Papanikolas, M. D. Rogers, D. Samart, “The Mahler measure of a Calabi-Yau threefold and special $L$-values”, Math. Z., 276:3-4 (2014), 1151–1163  crossref  mathscinet  zmath  isi  scopus
    6. E. Shinder, M. Vlasenko, “Mahler measures and double L-values of modular forms”, J. Number Theory, 142 (2014), 149–182  crossref  mathscinet  zmath  isi  scopus
    7. W. Zudilin, “Two hypergeometric tales and a new irrationality measure of $\zeta(2)$”, Ann. Math. Qué., 38:1 (2014), 101–117  crossref  mathscinet  zmath
    8. S. Dauguet, W. Zudilin, “On simultaneous diophantine approximations to $\zeta(2)$ and $\zeta(3)$”, J. Number Theory, 145 (2014), 362–387  crossref  mathscinet  zmath  isi  elib  scopus
    9. E. A. Karatsuba, “On One method for constructing a family of approximations of zeta constants by rational fractions”, Problems Inform. Transmission, 51:4 (2015), 378–390  mathnet  crossref  isi  elib
    10. Bartlett N., Warnaar S.O., “Hall–Littlewood polynomials and characters of affine Lie algebras”, Adv. Math., 285 (2015), 1066–1105  crossref  mathscinet  zmath  isi  elib  scopus
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