Geodesic
The Poincare Series and Operators of Duality for Multiplicative Automorphic Forms
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 13 (2013) no. 3, pp. 103-112

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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.
Keywords: multiplicative automorphic forms, integral operators of Bers, bilinear pairings, series Poincare, duality
Mots-clés : conjugation. 
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     author = {O. A. Sergeeva},
     title = {The {Poincare} {Series} and {Operators} of {Duality} for {Multiplicative} {Automorphic} {Forms}},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {103--112},
     publisher = {mathdoc},
     volume = {13},
     number = {3},
     year = {2013},
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     url = {http://geodesic.mathdoc.fr/item/VNGU_2013_13_3_a9/}
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O. A. Sergeeva. The Poincare Series and Operators of Duality for Multiplicative Automorphic Forms. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 13 (2013) no. 3, pp. 103-112. http://geodesic.mathdoc.fr/item/VNGU_2013_13_3_a9/