@article{938419,
      recid = {938419},
      author = {Gritsenko, Valery A. and Spiridonov, V. P.},
      title = {Partition functions and automorphic forms /},
      publisher = {Springer,},
      address = {Cham :},
      pages = {1 online resource},
      year = {2020},
      abstract = {This book offers an introduction to the research in  several recently discovered and actively developing  mathematical and mathematical physics areas. It focuses on:  1) Feynman integrals and modular functions, 2) hyperbolic  and Lorentzian Kac-Moody algebras, related automorphic  forms and applications to quantum gravity, 3)  superconformal indices and elliptic hypergeometric  integrals, related instanton partition functions, 4)  moonshine, its arithmetic aspects, Jacobi forms, elliptic  genus, and string theory, and 5) theory and applications of  the elliptic Painleve equation, and aspects of Painleve  equations in quantum field theories. All the topics covered  are related to various partition functions emerging in  different supersymmetric and ordinary quantum field  theories in curved space-times of different (d=2,3,...,6)  dimensions. Presenting multidisciplinary methods  (localization, Borcherds products, theory of special  functions, Cremona maps, etc) for treating a range of  partition functions, the book is intended for graduate  students and young postdocs interested in the interaction  between quantum field theory and mathematics related to  automorphic forms, representation theory, number theory and  geometry, and mirror symmetry.},
      url = {http://library.usi.edu/record/938419},
      doi = {https://doi.org/10.1007/978-3-030-42},
}