Volkov's Pentagon for the Modular Quantum Dilogarithm

Abstract

The new form of pentagon equations suggested by Volkov for the $ q $-exponential on the basis of formal series is derived within the Hilbert space framework for the modular version of the quantum dilogarithm.

extended version of paper published in journal "Functional Analysis and Applications" vol.45(4), 2011, p.65 (in Russian)