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Izv. Akad. Nauk SSSR Ser. Mat., 1989, Volume 53, Issue 6, Pages 1206–1235 (Mi izv1154)  

This article is cited in 14 scientific papers (total in 14 papers)

The Euler beta-function, the Vandermonde determinant, Legendre's equation, and critical values of linear functions on a configuration of hyperplanes. I

A. N. Varchenko


Abstract: When working with a set of linear functions and the configration of hyperplanes they define, one encounters a matrix of multidimensional hypergeometric integrals. We give a formula which expresses the determinant of this matrix in terms of critical values of the linear functions restricted to the configuration.
Bibliography: 26 titles.

Full text: PDF file (3534 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1990, 35:3, 543–571

Bibliographic databases:

UDC: 517.95
MSC: Primary 14H05, 33A35; Secondary 05B30, 14K20, 35G20, 33A15
Received: 26.04.1988

Citation: A. N. Varchenko, “The Euler beta-function, the Vandermonde determinant, Legendre's equation, and critical values of linear functions on a configuration of hyperplanes. I”, Izv. Akad. Nauk SSSR Ser. Mat., 53:6 (1989), 1206–1235; Math. USSR-Izv., 35:3 (1990), 543–571

Citation in format AMSBIB
\Bibitem{Var89}
\by A.~N.~Varchenko
\paper The Euler beta-function, the Vandermonde determinant, Legendre's equation, and critical values of linear functions on a~configuration of hyperplanes.~I
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1989
\vol 53
\issue 6
\pages 1206--1235
\mathnet{http://mi.mathnet.ru/izv1154}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1039962}
\zmath{https://zbmath.org/?q=an:0709.33001|0695.33004}
\transl
\jour Math. USSR-Izv.
\yr 1990
\vol 35
\issue 3
\pages 543--571
\crossref{https://doi.org/10.1070/IM1990v035n03ABEH000717}


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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. A. N. Varchenko, “The Euler beta-function, the Vandermonde determinant, Legendre's equation, and critical values of linear functions on a configuration of hyperplanes. II”, Math. USSR-Izv., 36:1 (1991), 155–167  mathnet  crossref  mathscinet  zmath  adsnasa
    2. A. N. Varchenko, “Determinant formula for Selberg-type integrals”, Funct. Anal. Appl., 25:4 (1991), 304–305  mathnet  crossref  mathscinet  zmath  isi
    3. Philippe Jacobs, Ann Laeremans, “Arrangements with one bounded component andp-adic integrals”, manuscripta math, 85:1 (1994), 33  crossref  mathscinet  zmath  isi
    4. Antoine Douai, Hiroaki Terao, “The determinant of a hypergeometric period matrix”, Invent math, 128:3 (1997), 417  crossref  mathscinet  zmath  isi  elib
    5. V. Tarasov, A. Varchenko, “Geometry of q-hypergeometric functions as a bridge between Yangians and quantum affine algebras”, Invent math, 128:3 (1997), 501  crossref  mathscinet  zmath  adsnasa  isi
    6. T. Brylawski, A. Varchenko, “The Determinant Formula for a Matroid Bilinear Form”, Advances in Mathematics, 129:1 (1997), 1  crossref
    7. Kazuhiko Aomoto, Michitake Kita, Peter Orlik, Hiroaki Terao, “Twisted de Rham Cohomology Groups of Logarithmic Forms”, Advances in Mathematics, 128:1 (1997), 119  crossref
    8. T. Brylawski, “A Möbius Identity Arising from Modularity in a Matroid Bilinear Form”, Journal of Combinatorial Theory, Series A, 91:1-2 (2000), 622  crossref
    9. S. A. Yuzvinskii, “Orlik–Solomon algebras in algebra and topology”, Russian Math. Surveys, 56:2 (2001), 293–364  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    10. Byungheup Jun, “Period determinant of an irregular connection over an elliptic curve”, Journal of Algebra, 291:2 (2005), 325  crossref
    11. D. Mukherjee, Alexander Varchenko, “Determinants of the Hypergeometric Period Matrices of an Arrangement and Its Dual”, Ann Combin, 2009  crossref  isi
    12. E. M. Rains, V. P. Spiridonov, “Determinants of Elliptic Hypergeometric Integrals”, Funct. Anal. Appl., 43:4 (2009), 297–311  mathnet  crossref  crossref  mathscinet  zmath  isi
    13. Peter J. Forrester, Eric M. Rains, “A Fuchsian Matrix Differential Equation for Selberg Correlation Integrals”, Commun. Math. Phys, 2011  crossref
    14. Richárd Rimányi, Vadim Schechtman, Alexander Varchenko, “Conformal blocks and equivariant cohomology”, Mosc. Math. J., 11:3 (2011), 561–581  mathnet  mathscinet
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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