Geodesic
General Modular Quantum Dilogarithm and Beta Integrals
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mathematical and theoretical physics, Tome 309 (2020), pp. 269-289

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We consider a univariate beta integral composed of general modular quantum dilogarithm functions and prove its exact evaluation formula. It represents the partition function of a particular 3d supersymmetric field theory on the general squashed lens space. Its possible applications to 2d conformal field theory are briefly discussed as well. 
@article{TM_2020_309_a18,
     author = {Gor A. Sarkissian and Vyacheslav P. Spiridonov},
     title = {General {Modular} {Quantum} {Dilogarithm} and {Beta} {Integrals}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {269--289},
     publisher = {mathdoc},
     volume = {309},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2020_309_a18/}
}
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Gor A. Sarkissian; Vyacheslav P. Spiridonov. General Modular Quantum Dilogarithm and Beta Integrals. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mathematical and theoretical physics, Tome 309 (2020), pp. 269-289. http://geodesic.mathdoc.fr/item/TM_2020_309_a18/