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Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 2013, Volume 13, Issue 3, Pages 103–112 (Mi vngu158)  
The Poincare Series and Operators of Duality for Multiplicative Automorphic Forms

O. A. Sergeeva

Kemerovo State University

Abstract: 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, conjugation.

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English version:
Journal of Mathematical Sciences, 2015, 205:3, 445–454

UDC: 517.54:517.862
Received: 22.11.2012

Citation: O. A. Sergeeva, “The Poincare Series and Operators of Duality for Multiplicative Automorphic Forms”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 13:3 (2013), 103–112; J. Math. Sci., 205:3 (2015), 445–454

Citation in format AMSBIB
\Bibitem{Ser13}
\by O.~A.~Sergeeva
\paper The Poincare Series and Operators of Duality for Multiplicative Automorphic Forms
\jour Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform.
\yr 2013
\vol 13
\issue 3
\pages 103--112
\mathnet{http://mi.mathnet.ru/vngu158}
\transl
\jour J. Math. Sci.
\yr 2015
\vol 205
\issue 3
\pages 445--454
\crossref{https://doi.org/10.1007/s10958-015-2258-z}


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    		• Вестник Новосибирского государственного университета. Серия: математика, механика, информатика
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