V. P. Spiridonov, “Theta hypergeometric integrals”, Algebra i Analiz, 15:6 (2003), 161–215; St. Petersburg Math. J., 15:6 (2004), 929

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Algebra i Analiz, 2003, Volume 15, Issue 6, Pages 161–215 (Mi aa829)

This article is cited in 99 scientific papers (total in 99 papers)

Research Papers

Theta hypergeometric integrals

V. P. Spiridonov

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

Full-text PDF (2549 kB) Citations (99)

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Abstract: 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}

$A_n$ and

C_{n}

$C_n$ is described. Some of the

C_{n}

$C_n$ -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.

Received: 15.03.2003

English version:
St. Petersburg Mathematical Journal, 2004, Volume 15, Issue 6, Pages 929–967
DOI: https://doi.org/10.1090/S1061-0022-04-00839-8

Bibliographic databases:

Document Type: Article

Language: English

Citation: V. P. Spiridonov, “Theta hypergeometric integrals”, Algebra i Analiz, 15:6 (2003), 161–215; St. Petersburg Math. J., 15:6 (2004), 929–967

Citation in format AMSBIB

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\jour St. Petersburg Math. J.

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\crossref{https://doi.org/10.1090/S1061-0022-04-00839-8}

Linking options:

https://www.mathnet.ru/eng/aa829

https://www.mathnet.ru/eng/aa/v15/i6/p161

This publication is cited in the following 99 articles:

Nikita Belousov, Sergey Derkachov, Sergey Kharchev, Sergey Khoroshkin, “Baxter Operators in Ruijsenaars Hyperbolic System IV: Coupling Constant Reflection Symmetry”, Commun. Math. Phys., 405:4 (2024)
Elena Apresyan, Gor Sarkissian, “S-move matrix in the NS sector of N = 1 super Liouville field theory”, J. High Energ. Phys., 2024:7 (2024)
Mourad E.H. Ismail, Eric M. Rains, Dennis Stanton, “Orthogonality of very well-poised series”, Indagationes Mathematicae, 2024
D. I. Krotkov, V. P. Spiridonov, “Infinite elliptic hypergeometric series: convergence and difference equations”, Sb. Math., 214:12 (2023), 1751–1778
Elena Apresyan, Gor Sarkissian, Vyacheslav P. Spiridonov, “A parafermionic hypergeometric function and supersymmetric 6j-symbols”, Nuclear Physics B, 990 (2023), 116170
Farrokh Atai, Masatoshi Noumi, “Eigenfunctions of the van Diejen model generated by gauge and integral transformations”, Advances in Mathematics, 412 (2023), 108816
Stephane Bajeot, Sergio Benvenuti, Matteo Sacchi, “S-confining gauge theories and supersymmetry enhancements”, J. High Energ. Phys., 2023:8 (2023)
A. V. Ivanov, “On Gustafson Integrals for the Group SL(2, ℝ)”, J Math Sci, 275:3 (2023), 299
G. A. Sarkissian, V. P. Spiridonov, “Elliptic and Complex Hypergeometric Integrals in Quantum Field Theory”, Phys. Part. Nuclei Lett., 20:3 (2023), 281
S. E. Derkachov, G. A. Sarkissian, V. P. Spiridonov, “Elliptic hypergeometric function and $6j$ -symbols for the $SL(2,\pmb{\mathbb C})$ group”, Theoret. and Math. Phys., 213:1 (2022), 1406–1422
Lea E. Bottini, Chiung Hwang, Sara Pasquetti, Matteo Sacchi, “Dualities from dualities: the sequential deconfinement technique”, J. High Energ. Phys., 2022:5 (2022)
Martin Hallnäs, Edwin Langmann, Masatoshi Noumi, Hjalmar Rosengren, “Higher Order Deformed Elliptic Ruijsenaars Operators”, Commun. Math. Phys., 392:2 (2022), 659
G A Sarkissian, V P Spiridonov, “Complex hypergeometric functions and integrable many-body problems”, J. Phys. A: Math. Theor., 55:38 (2022), 385203
Roussillon J., “The Virasoro Fusion Kernel and Ruijsenaars' Hypergeometric Function”, Lett. Math. Phys., 111:1 (2021), 7
A. V. Ivanov, “Ob integralakh Gustafsona dlya gruppy $\mathrm{SL}(2,\mathbb{R})$ ”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 28, Zap. nauchn. sem. POMI, 509, POMI, SPb., 2021, 113–122
Sergey È. Derkachov, Alexander N. Manashov, “On Complex Gamma-Function Integrals”, SIGMA, 16 (2020), 003, 20 pp.
Gor A. Sarkissian, Vyacheslav P. Spiridonov, “The Endless Beta Integrals”, SIGMA, 16 (2020), 074, 21 pp.
Spiridonov V.P., “Superconformal Indices, Seiberg Dualities and Special Functions”, Phys. Part. Nuclei, 51:4 (2020), 508–513
Ardehali A.A., “Cardy-Like Asymptotics of the 4D N=4 Index and Ads(5) Blackholes”, J. High Energy Phys., 2019, no. 6, 134
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

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