The Poincare Series and Operators of Duality for Multiplicative Automorphic Forms

The establishing connection between bilinear pairings of dual $(q,\rho)$-forms formulas and properties of a self-conjugation for operators of duality (of Bers) and their conjugation with each other concerning these bilinear pairings are proved. Using these formulas and properties of the spaces of multiplicative automorphic forms in case of inessential character we prove the properties of a commutativity of operators of a duality with the setting of multiplicative Poincare series mapping and other properties of this mapping.