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Funktsional. Anal. i Prilozhen., 1989, Volume 23, Issue 2, Pages 12–26 (Mi faa1015)  

This article is cited in 23 scientific papers (total in 23 papers)

Hypergeometric functions and toral manifolds

I. M. Gel'fand, A. V. Zelevinskii, M. M. Kapranov


Full text: PDF file (1867 kB)
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English version:
Functional Analysis and Its Applications, 1989, 23:2, 94–106

Bibliographic databases:

UDC: 517.95
Received: 02.11.1988

Citation: I. M. Gel'fand, A. V. Zelevinskii, M. M. Kapranov, “Hypergeometric functions and toral manifolds”, Funktsional. Anal. i Prilozhen., 23:2 (1989), 12–26; Funct. Anal. Appl., 23:2 (1989), 94–106

Citation in format AMSBIB
\Bibitem{GelZelKap89}
\by I.~M.~Gel'fand, A.~V.~Zelevinskii, M.~M.~Kapranov
\paper Hypergeometric functions and toral manifolds
\jour Funktsional. Anal. i Prilozhen.
\yr 1989
\vol 23
\issue 2
\pages 12--26
\mathnet{http://mi.mathnet.ru/faa1015}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1011353}
\zmath{https://zbmath.org/?q=an:0721.33006}
\transl
\jour Funct. Anal. Appl.
\yr 1989
\vol 23
\issue 2
\pages 94--106
\crossref{https://doi.org/10.1007/BF01078777}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1989CH31600002}


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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. R. Askey, “Ramanujan and hypergeometric and basic hypergeometric series”, Russian Math. Surveys, 45:1 (1990), 37–86  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. I. M. Gel'fand, A. V. Zelevinskii, M. M. Kapranov, “Discriminants of polynomials in many variables”, Funct. Anal. Appl., 24:1 (1990), 1–4  mathnet  crossref  mathscinet  zmath  isi
    3. M. I. Graev, “General hypergeometric functions”, Funct. Anal. Appl., 26:2 (1992), 131–133  mathnet  crossref  mathscinet  zmath  isi
    4. I. M. Gel'fand, M. I. Graev, V. S. Retakh, “General hypergeometric systems of equations and series of hypergeometric type”, Russian Math. Surveys, 47:4 (1992), 1–88  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    5. I. M. Gel'fand, A. V. Zelevinskii, M. M. Kapranov, “A Correction to the Paper “Hypergeometric Functions and Toric Varieties””, Funct. Anal. Appl., 27:4 (1993), 295–295  mathnet  crossref  mathscinet  zmath  isi
    6. D. V. Yur'ev, “Quantum projective field theory: Quantum-field analogs of the Euler–Arnol'd equations in projective $G$ multiplets”, Theoret. and Math. Phys., 98:2 (1994), 147–161  mathnet  crossref  mathscinet  zmath  isi
    7. M. Passare, A. K. Tsikh, A. A. Cheshel, “Iterated Mellin–Barnes integrals as periods on the Calabi–Yau manifolds with several modules”, Theoret. and Math. Phys., 109:3 (1996), 1544–1555  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. I. M. Gel'fand, M. I. Graev, “$GG$-functions and their relation to general hypergeometric functions”, Russian Math. Surveys, 52:4 (1997), 639–684  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    9. I. M. Gel'fand, M. I. Graev, V. S. Retakh, “General gamma functions, exponentials, and hypergeometric functions”, Russian Math. Surveys, 53:1 (1998), 1–55  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    10. I. M. Gel'fand, M. I. Graev, “$\mathscr N$-functions and their relationship with solutions of general hypergeometric systems and $GG$-systems”, Russian Math. Surveys, 56:4 (2001), 615–647  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    11. I. M. Gel'fand, M. I. Graev, V. S. Retakh, “Hypergeometric functions over an arbitrary field”, Russian Math. Surveys, 59:5 (2004), 831–905  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    12. A. Dickenstein, T. M. Sadykov, “Bases in the solution space of the Mellin system”, Sb. Math., 198:9 (2007), 1277–1298  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    13. Vitaly A. Krasikov, Timur M. Sadykov, “The Newton polytope of the optimal differential operator for an algebraic curve”, Zhurn. SFU. Ser. Matem. i fiz., 6:2 (2013), 200–210  mathnet
    14. A. V. Stoyanovskii, “$A$-Hypergeometric Functions in Transcendental Questions of Algebraic Geometry”, Funct. Anal. Appl., 48:1 (2014), 76–78  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    15. V. R. Kulikov, V. A. Stepanenko, “On solutions and Waring's formulae for the system of $n$ algebraic equations with $n$ unknowns”, St. Petersburg Math. J., 26:5 (2015), 839–848  mathnet  crossref  mathscinet  isi  elib  elib
    16. V. A. Klyachin, “Ekstremalnye svoistva triangulyatsii, osnovannoi na uslovii pustogo vypuklogo mnozhestva”, Sib. elektron. matem. izv., 12 (2015), 991–997  mathnet  crossref
    17. T. M. Sadykov, S. Tanabé, “Maximally reducible monodromy of bivariate hypergeometric systems”, Izv. Math., 80:1 (2016), 221–262  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    18. D. V. Artamonov, “The Stokes phenomenon for an irregular Gelfand-Kapranov-Zelevinsky system associated with a rank one lattice”, Sb. Math., 207:8 (2016), 1037–1063  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    19. Jie Zhou, “GKZ Hypergeometric Series for the Hesse Pencil, Chain Integrals and Orbifold Singularities”, SIGMA, 13 (2017), 030, 32 pp.  mathnet  crossref
    20. V. A. Klyachin, M. I. Kazanin, “Postroenie reshenii uravneniya tipa Monzha–Ampera na osnove $\Phi$-triangulyatsii”, Vestn. Volgogr. gos. un-ta. Ser. 1, Mat. Fiz., 2017, no. 1(38), 6–12  mathnet  crossref
    21. Shinobu Hosono, Hiromichi Takagi, “Movable vs Monodromy Nilpotent Cones of Calabi–Yau Manifolds”, SIGMA, 14 (2018), 039, 37 pp.  mathnet  crossref
    22. S. I. Bezrodnykh, “The Lauricella hypergeometric function $F_D^{(N)}$, the Riemann–Hilbert problem, and some applications”, Russian Math. Surveys, 73:6 (2018), 941–1031  mathnet  crossref  crossref  adsnasa  isi  elib
    23. Lisa Nilsson, Mikael Passare, August K. Tsikh, “Domains of convergence for $A$-hypergeometric series and integrals”, Zhurn. SFU. Ser. Matem. i fiz., 12:4 (2019), 509–529  mathnet  crossref
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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