?
Introduction to the theory of elliptic hypergeometric integrals
P. 271–318.
Publication based on the results of:
Spiridonov V., Кротков Д. И., / Series arXiv "math". 2023. No. 08002.
We derive finite difference equations of infinite order for theta hypergeometric series and investigate the space of their solutions. In general, such infinite series diverge, we describe some constraints on the parameters when they do converge. In particular, we lift the Hardy-Littlewood criterion on the convergence of q-hypergeometric series for |q|=1,qn≠1, to the elliptic level and prove ...
Added: July 26, 2023
Springer Publishing Company, 2020.
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) ...
Added: September 9, 2020
Spiridonov V., Brunner F., Regalado D., Journal of High Energy Physics 2017 No. 07 P. 1–20
We provide a recipe to extract the supersymmetric Casimir energy of theories
defined on primary Hopf surfaces directly from the superconformal index. It involves an
SL(3, Z) transformation acting on the complex structure moduli of the background geometry.
In particular, the known relation between Casimir energy, index and partition
function emerges naturally from this framework, allowing rewriting of the ...
Added: July 31, 2017