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Uspekhi Mat. Nauk, 2004, Volume 59, Issue 5(359), Pages 29–100 (Mi umn771)  

This article is cited in 8 scientific papers (total in 9 papers)

Hypergeometric functions over an arbitrary field

I. M. Gel'fand, M. I. Graev, V. S. Retakh

Scientific Research Institute for System Studies of RAS

Abstract: This paper is devoted to the definition and investigation of hypergeometric functions over an arbitrary continuous locally compact field or a finite field, based on the author's earlier definition of generalized hypergeometric function over the field $\mathbb R$.

DOI: https://doi.org/10.4213/rm771

Full text: PDF file (639 kB)
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English version:
Russian Mathematical Surveys, 2004, 59:5, 831–905

Bibliographic databases:

UDC: 517.58
MSC: Primary 33C70; Secondary 33C80, 33C20, 12J25, 12E20, 46S10, 33C05, 33D70
Received: 12.07.2004

Citation: I. M. Gel'fand, M. I. Graev, V. S. Retakh, “Hypergeometric functions over an arbitrary field”, Uspekhi Mat. Nauk, 59:5(359) (2004), 29–100; Russian Math. Surveys, 59:5 (2004), 831–905

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. R. S. Ismagilov, “Racah operators for principal series of representations of the group $\mathrm {SL}(2,\mathbb C)$”, Sb. Math., 198:3 (2007), 369–381  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. Kochubei A.N., “Evolution equations and functions of hypergeometric type over fields of positive characteristic”, Bull. Belg. Math. Soc. Simon Stevin, 14:5 (2007), 947–959  mathscinet  zmath  isi  elib
    3. A. M. Vershik, I. M. Gel'fand, S. G. Gindikin, A. A. Kirillov, G. L. Litvinov, V. F. Molchanov, Yu. A. Neretin, V. S. Retakh, “Mark Iosifovich Graev (to his 85th brithday)”, Russian Math. Surveys, 63:1 (2008), 173–188  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. Osburn R., Schneider C., “Gaussian hypergeometric series and supercongruences”, Math. Comp., 78:265 (2009), 275–292  crossref  mathscinet  zmath  adsnasa  isi
    5. Miyatani K., Sano M., “An Exponential Sum and Higher-Codimensional Subvarieties of Projective Spaces Over Finite Fields”, Hiroshima Math. J., 44:3 (2014), 327–340  mathscinet  zmath  isi
    6. Fu L., “-adic GKZ hypergeometric sheaves and exponential sums”, Adv. Math., 298 (2016), 51–88  crossref  mathscinet  zmath  isi  elib  scopus
    7. Nie M., “Zeta functions of trinomial curves and maximal curves”, Finite Fields their Appl., 39 (2016), 52–82  crossref  mathscinet  zmath  isi  elib  scopus
    8. Derkachov S.E., Manashov A.N., Valinevich P.A., “Gustafson Integrals For Sl(2, C) Spin Magnet”, J. Phys. A-Math. Theor., 50:29 (2017), 294007  crossref  mathscinet  zmath  isi
    9. Sergey É. Derkachov, Alexander N. Manashov, Pavel A. Valinevich, “$\mathrm{SL}(2,\mathbb{C})$ Gustafson Integrals”, SIGMA, 14 (2018), 030, 16 pp.  mathnet  crossref
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