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Алгебра и анализ, 2003, том 15, выпуск 6, страницы 161–215 (Mi aa829)  

Эта публикация цитируется в 78 научных статьях (всего в 78 статьях)

Статьи

Theta hypergeometric integrals

V. P. Spiridonov

Bogolyubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Moscow Region, Dubna, Russia

Аннотация: A general class of (multiple) hypergeometric type integrals associated with the Jacobi theta functions is defined. These integrals are related to theta hypergeometric series via the residue calculus. In the one variable case, theta function extensions of the Meijer function are obtained. A number of multiple generalizations of the elliptic beta integral [S2] associated with the root systems $A_n$ and $C_n$ is described. Some of the $C_n$-examples were proposed earlier by van Diejen and the author, but other integrals are new. An example of the biorthogonality relations associated with the elliptic beta integrals is considered in detail.

Полный текст: PDF файл (2549 kB)
Список литературы: PDF файл   HTML файл

Англоязычная версия:
St. Petersburg Mathematical Journal, 2004, 15:6, 929–967

Реферативные базы данных:

Поступила в редакцию: 15.03.2003
Язык публикации: английский

Образец цитирования: V. P. Spiridonov, “Theta hypergeometric integrals”, Алгебра и анализ, 15:6 (2003), 161–215; St. Petersburg Math. J., 15:6 (2004), 929–967

Цитирование в формате AMSBIB
\RBibitem{Spi03}
\by V.~P.~Spiridonov
\paper Theta hypergeometric integrals
\jour Алгебра и анализ
\yr 2003
\vol 15
\issue 6
\pages 161--215
\mathnet{http://mi.mathnet.ru/aa829}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2044635}
\zmath{https://zbmath.org/?q=an:1071.33011}
\transl
\jour St. Petersburg Math. J.
\yr 2004
\vol 15
\issue 6
\pages 929--967
\crossref{https://doi.org/10.1090/S1061-0022-04-00839-8}


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    Citing articles on Google Scholar: Russian citations, English citations
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    Эта публикация цитируется в следующих статьяx:
    1. В. П. Спиридонов, “Дерево Бэйли для интегралов”, ТМФ, 139:1 (2004), 104–111  mathnet  crossref  mathscinet  zmath  adsnasa; V. P. Spiridonov, “A Bailey Tree for Integrals”, Theoret. and Math. Phys., 139:1 (2004), 536–541  crossref  isi  elib
    2. Spiridonov V. P., Zhedanov A. S., “Poisson algebras for some generalized eigenvalue problems”, J. Phys. A, 37:43 (2004), 10429–10443  crossref  mathscinet  zmath  adsnasa  isi  scopus
    3. Krattenthaler C., “Advanced determinant calculus: A complement”, Linear Algebra Appl., 411 (2005), 68–166  crossref  mathscinet  zmath  isi  elib  scopus
    4. Warnaar S. O., “Summation formulae for elliptic hypergeometric series”, Proc. Amer. Math. Soc., 133:2 (2005), 519–527 (electronic)  crossref  mathscinet  zmath  isi  elib  scopus
    5. Van Diejen JF, Spiridonov VP, “Unit circle elliptic beta integrals”, Ramanujan J., 10:2 (2005), 187–204  crossref  zmath  isi  scopus
    6. Rosengren H., “New transformations for elliptic hypergeometric series on the root system $A_n$”, Ramanujan J., 12:2 (2006), 155–166  crossref  mathscinet  zmath  isi  scopus
    7. Spiridonov V. P., Warnaar S. O., “Inversions of integral operators and elliptic beta integrals on root systems”, Adv. Math., 207:1 (2006), 91–132  crossref  mathscinet  zmath  isi  elib  scopus
    8. Rains E. M., “$BC_n$-symmetric Abelian functions”, Duke Math. J., 135:1 (2006), 99–180  crossref  mathscinet  zmath  isi  elib  scopus
    9. Rosengren H., Schlosser M., “Elliptic determinant evaluations and the Macdonald identities for affine root systems”, Compos. Math., 142:4 (2006), 937–961  crossref  mathscinet  zmath  isi  elib  scopus
    10. Spiridonov V.P., “A multiparameter summation formula for Riemann theta functions”, Jack, Hall-Littlewood and Macdonald Polynomials, Contemporary Mathematics Series, 417, 2006, 345–353  crossref  mathscinet  zmath  isi
    11. В. П. Спиридонов, “Эллиптические гипергеометрические функции и модели типа Калоджеро–Сазерленда”, ТМФ, 150:2 (2007), 311–324  mathnet  crossref  mathscinet  zmath  adsnasa  elib; V. P. Spiridonov, “Elliptic hypergeometric functions and Calogero–Sutherland-type models”, Theoret. and Math. Phys., 150:2 (2007), 266–277  crossref  isi  elib
    12. van de Bult F. J., Rains E. M., Stokman J. V., “Properties of generalized univariate hypergeometric functions”, Comm. Math. Phys., 275:1 (2007), 37–95  crossref  mathscinet  zmath  adsnasa  isi  scopus
    13. Spiridonov V. P., “Short proofs of the elliptic beta integrals”, Ramanujan J., 13:1-3 (2007), 265–283  crossref  mathscinet  zmath  isi  scopus
    14. Spiridonov V. P., Zhedanov A. S., “Elliptic grids, rational functions, and the Padé interpolation”, Ramanujan J., 13:1-3 (2007), 285–310  crossref  mathscinet  zmath  isi  scopus
    15. Rosengren H., “An elementary approach to $6j$-symbols (classical, quantum, rational, trigonometric, and elliptic)”, Ramanujan J., 13:1-3 (2007), 131–166  crossref  mathscinet  zmath  isi  scopus
    16. Gasper G., Rahman M., “Some systems of multivariable orthogonal $q$-Racah polynomials”, Ramanujan J., 13:1-3 (2007), 389–405  crossref  mathscinet  zmath  isi  scopus
    17. В. П. Спиридонов, “Очерки теории эллиптических гипергеометрических функций”, УМН, 63:3(381) (2008), 3–72  mathnet  crossref  mathscinet  zmath  adsnasa  elib; V. P. Spiridonov, “Essays on the theory of elliptic hypergeometric functions”, Russian Math. Surveys, 63:3 (2008), 405–472  crossref  isi  elib
    18. В. П. Спиридонов, “Непрерывная биортогональность эллиптической гипергеометрической функции”, Алгебра и анализ, 20:5 (2008), 155–185  mathnet  mathscinet  zmath  elib; V. P. Spiridonov, “Continuous biorthogonality of the elliptic hypergeometric function”, St. Petersburg Math. J., 20:5 (2009), 791–812  crossref  isi
    19. Chu Wenchang, Jia Cangzhi, “Abel's method on summation by parts and theta hypergeometric series”, J. Combin. Theory Ser. A, 115:5 (2008), 815–844  crossref  mathscinet  zmath  isi  elib  scopus
    20. Schlosser M.J., “A Taylor expansion theorem for an elliptic extension of the Askey–Wilson operator”, Special Functions and Orthogonal Polynomials, Contemporary Mathematics Series, 471, 2008, 175–186  crossref  mathscinet  zmath  isi
    21. Fokko J. van de Bult, Eric M. Rains, “Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions”, SIGMA, 5 (2009), 059, 31 pp.  mathnet  crossref  mathscinet
    22. Э. М. Райнс, В. П. Спиридонов, “Определители эллиптических гипергеометрических интегралов”, Функц. анализ и его прил., 43:4 (2009), 67–86  mathnet  crossref  mathscinet  zmath; E. M. Rains, V. P. Spiridonov, “Determinants of Elliptic Hypergeometric Integrals”, Funct. Anal. Appl., 43:4 (2009), 297–311  crossref  isi
    23. Magnus A. P., “Rational interpolation to solutions of Riccati difference equations on elliptic lattices”, J. Comput. Appl. Math., 233:3 (2009), 793–801  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    24. Chu Wenchang, Jia Cangzhi, “Abel's method on summation by parts for elliptic hypergeometric series”, Commun. Contemp. Math., 11:3 (2009), 337–353  crossref  mathscinet  zmath  isi  scopus
    25. Spiridonov V. P., “Superconformal indices for $N=1$ theories with multiple duals”, Nuclear Physics B, 824:1-2 (2010), 192–216  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    26. Spiridonov V.P., Vartanov G.S., “Supersymmetric Dualities beyond the Conformal Window”, Physical Review Letters, 105:6 (2010), 061603  crossref  mathscinet  adsnasa  isi  elib  scopus
    27. Rains E.M., “Transformations of elliptic hypergeometric integrals”, Annals of Mathematics, 171:1 (2010), 169–243  crossref  mathscinet  zmath  isi  scopus
    28. Khmelnitsky A., “Interpreting multiple dualities conjectured from superconformal index identities”, Journal of High Energy Physics, 2010, no. 3, 065  crossref  mathscinet  zmath  isi  scopus
    29. Spiridonov V.P., Vartanov G.S., “Elliptic Hypergeometry of Supersymmetric Dualities”, Comm Math Phys, 304:3 (2011), 797–874  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    30. Spiridonov V.P., Warnaar S.O., “New multiple (6)psi(6) summation formulas and related conjectures”, Ramanujan J, 25:3 (2011), 319–342  crossref  mathscinet  zmath  isi  scopus
    31. Dolan F.A.H., Spiridonov V.P., Vartanov G.S., “From 4d superconformal indices to 3d partition functions”, Phys Lett B, 704:3 (2011), 234–241  crossref  mathscinet  adsnasa  isi  elib  scopus
    32. Nakayama Yu., “4D and 2D superconformal index with surface operator”, Journal of High Energy Physics, 2011, no. 8, 084  crossref  mathscinet  zmath  isi  scopus
    33. Rosengren H., “Felder's Elliptic Quantum Group and Elliptic Hypergeometric Series on the Root System A(n)”, Int Math Res Not, 2011, no. 13, 2861–2920  mathscinet  zmath  isi  elib
    34. Gadde A., Rastelli L., Razamat Sh.S., Yan W., “On the superconformal index of N=1 IR fixed points. A holographic check”, Journal of High Energy Physics, 2011, no. 3, 041  crossref  mathscinet  zmath  isi  scopus
    35. van de Bult F.J., “An elliptic hypergeometric integral with W(F (4)) symmetry”, Ramanujan J, 25:1 (2011), 1–20  crossref  mathscinet  isi  scopus
    36. Vartanov G.S., “On the ISS model of dynamical SUSY breaking”, Phys Lett B, 696:3 (2011), 288–290  crossref  mathscinet  adsnasa  isi  elib  scopus
    37. Morita T., Niarchos V., “F-theorem, duality and SUSY breaking in one-adjoint Chern–Simons-Matter theories”, Nuclear Phys B, 858:1 (2012), 84–116  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    38. Dimofte T., Gaiotto D., “An E-7 Surprise”, J. High Energy Phys., 2012, no. 10, 129  crossref  mathscinet  isi  elib  scopus
    39. Niarchos V., “Seiberg Dualities and the 3D/4D Connection”, J. High Energy Phys., 2012, no. 7, 075  crossref  mathscinet  isi  elib  scopus
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    41. Sudano M., “The Romelsberger Index, Berkooz Deconfinement, and Infinite Families of Seiberg Duals”, J. High Energy Phys., 2012, no. 5, 051  crossref  mathscinet  zmath  isi  scopus
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    43. Spiridonov V.P., “Elliptic Beta Integrals and Solvable Models of Statistical Mechanics”, Algebraic Aspects of Darboux Transformations, Quantum Integrable Systems and Supersymmetric Quantum Mechanics, Contemporary Mathematics, 563, ed. AcostaHumanez P. Finkel F. Kamran N. Olver P., Amer Mathematical Soc, 2012, 181–211  crossref  mathscinet  zmath  isi
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    46. Gahramanov I., Vartanov G., “Extended Global Symmetries for 4D N=1 SQCD Theories”, J. Phys. A-Math. Theor., 46:28 (2013), 285403  crossref  mathscinet  zmath  isi  elib  scopus
    47. Gahramanov I., Rosengren H., “A New Pentagon Identity for the Tetrahedron Index”, J. High Energy Phys., 2013, no. 11, 128  crossref  isi  elib  scopus
    48. Spiridonov V.P., Vartanov G.S., “Elliptic Hypergeometry of Supersymmetric Dualities II. Orthogonal Groups, Knots, and Vortices”, Commun. Math. Phys., 325:2 (2014), 421–486  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    49. Gerchkovitz E., “Constraints on the R-Charges of Free Bound States From the Romelsberger Index”, J. High Energy Phys., 2014, no. 7, 071  crossref  mathscinet  isi  elib  scopus
    50. Spiridonov V.P. Vartanov G.S., “Vanishing Superconformal Indices and the Chiral Symmetry Breaking”, J. High Energy Phys., 2014, no. 6, 062  crossref  isi  scopus
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    54. Gahramanov I.B., Vartanov G.S., “Superconformal Indices and Partition Functions For Supersymmetric Field Theories”, Xviith International Congress on Mathematical Physics, ed. Jensen A., World Scientific Publ Co Pte Ltd, 2014, 695–703  mathscinet  zmath  isi
    55. С. Э. Деркачёв, В. П. Спиридонов, “Конечномерные представления эллиптического модулярного дубля”, ТМФ, 183:2 (2015), 177–201  mathnet  crossref  mathscinet  adsnasa  elib; S. È. Derkachev, V. P. Spiridonov, “Finite-dimensional representations of the elliptic modular double”, Theoret. and Math. Phys., 183:2 (2015), 597–618  crossref  isi
    56. Stokman J., Vlaar B., “Koornwinder Polynomials and the Xxz Spin Chain”, J. Approx. Theory, 197:SI (2015), 69–100  crossref  mathscinet  zmath  isi  elib  scopus
    57. Gahramanov I. Spiridonov V.P., “the Star-Triangle Relation and 3D Superconformal Indices”, J. High Energy Phys., 2015, no. 8, 040  crossref  mathscinet  isi  elib  scopus
    58. Franco S., Hayashi H., Uranga A., “Charting Class S-K Territory”, Phys. Rev. D, 92:4 (2015), 045004  crossref  mathscinet  isi  elib  scopus
    59. van de Bult F.J., Rains E.M., “Limits of Elliptic Hypergeometric Biorthogonal Functions”, J. Approx. Theory, 193:SI (2015), 128–163  crossref  mathscinet  zmath  isi  scopus
    60. Maruyoshi K., Yagi J., “Surface defects as transfer matrices”, Prog. Theor. Exp. Phys., 2016, no. 11, 113B01  crossref  mathscinet  zmath  isi  elib  scopus
    61. Bruenner F., Spiridonov V.P., “A duality web of linear quivers”, Phys. Lett. B, 761 (2016), 261–264  crossref  zmath  isi  scopus
    62. Chicherin D. Derkachov S.E. Spiridonov V.P., “New Elliptic Solutions of the Yang–Baxter Equation”, Commun. Math. Phys., 345:2 (2016), 507–543  crossref  mathscinet  zmath  isi  elib  scopus
    63. Yagi J., “Branes and integrable lattice models”, Mod. Phys. Lett. A, 32:3 (2017), 1730003  crossref  mathscinet  zmath  isi  scopus
    64. Ito M., Noumi M., “Derivation of a
      $$BC_n$$
      B C n Elliptic Summation Formula via the Fundamental Invariants”, Constr. Approx., 45:1 (2017), 33–46  crossref  mathscinet  zmath  isi  scopus
    65. Hjalmar Rosengren, “Gustafson–Rakha-Type Elliptic Hypergeometric Series”, SIGMA, 13 (2017), 037, 11 pp.  mathnet  crossref
    66. Derkachov S.E., Manashov A.N., “Spin Chains and Gustafson'S Integrals”, J. Phys. A-Math. Theor., 50:29 (2017), 294006  crossref  mathscinet  zmath  isi  scopus
    67. Bruenner F., Regalado D., Spiridonov V.P., “Supersymmetric Casimir Energy and Sl(3, Z) Transformations”, J. High Energy Phys., 2017, no. 7, 041  crossref  mathscinet  isi  scopus
    68. Yagi J., “Surface Defects and Elliptic Quantum Groups”, J. High Energy Phys., 2017, no. 6, 013  crossref  mathscinet  isi  elib  scopus
    69. Bruenner F., Spiridonov V.P., “4D N=1 Quiver Gauge Theories and the a(N) Bailey Lemma”, J. High Energy Phys., 2018, no. 3, 105  crossref  mathscinet  zmath  isi  scopus
    70. Rosengren H., “Rahman'S Biorthogonal Rational Functions and Superconformal Indices”, Constr. Approx., 47:3 (2018), 529–552  crossref  mathscinet  zmath  isi  scopus
    71. Spiridonov V.P., “Rarefied Elliptic Hypergeometric Functions”, Adv. Math., 331 (2018), 830–873  crossref  mathscinet  zmath  isi  scopus
    72. Andrew P. Kels, Masahito Yamazaki, “Elliptic Hypergeometric Sum/Integral Transformations and Supersymmetric Lens Index”, SIGMA, 14 (2018), 013, 29 pp.  mathnet  crossref
    73. Sergey É. Derkachov, Alexander N. Manashov, Pavel A. Valinevich, “$\mathrm{SL}(2,\mathbb{C})$ Gustafson Integrals”, SIGMA, 14 (2018), 030, 16 pp.  mathnet  crossref
    74. Arash Arabi Ardehali, “The Hyperbolic Asymptotics of Elliptic Hypergeometric Integrals Arising in Supersymmetric Gauge Theory”, SIGMA, 14 (2018), 043, 30 pp.  mathnet  crossref
    75. Noumi M., “Remarks on Tau-Functions For the Difference Painleve Equations of Type E-8”, Representation Theory, Special Functions and Painleve Equations - Rims 2015, Advanced Studies in Pure Mathematics, 76, eds. Konno H., Sakai H., Shiraishi J., Suzuki T., Yamada Y., Math Soc Japan, 2018, 1–65  mathscinet  isi
    76. Gahramanov I. Jafarzade Sh., “Integrable Lattice Spin Models From Supersymmetric Dualities”, Phys. Part. Nuclei Lett., 15:6 (2018), 650–667  crossref  isi  scopus
    77. Bytsenko A.A., Chaichian M., Goncalves A.E., “Partition Functions For Supersymmetric Gauge Theories on Spheres”, Int. J. Mod. Phys. A, 33:30 (2018), 1850179  crossref  mathscinet  zmath  isi  scopus
    78. Ardehali A.A., “Cardy-Like Asymptotics of the 4D N=4 Index and Ads(5) Blackholes”, J. High Energy Phys., 2019, no. 6, 134  crossref  isi
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