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J. Sib. Fed. Univ. Math. Phys., 2011, Volume 4, Issue 1, Pages 128–139 (Mi jsfu170)  

This article is cited in 1 scientific paper (total in 1 paper)

The bilinear pairings for the holomorphic $(q,\rho)$-forms

Olga A. Sergeeva

Kemerovo State University, Kemerovo, Russia

Abstract: Study was started in [1, 2] of the normed spaces of multiplicative holomorphic automorphic forms for a Fuchsian group. In the present article bilinear pairings for general duality of the $(q,\rho)$-forms are considered. The symmetric variant of bilinear pairing which can be used in the theory of single-valued automorphic forms is received. On the basis of the entered bilinear pairings the modified integral Bers operators corresponding to them are investigated. These operators relate to a reflection in some quasicircle and also are connected to the general duality of $(q,\rho)$-forms. Under study the universal norm estimates for all operators is received.

Keywords: bilinear pairing, duality, multiplicative automorphic form, Bers operator.

Full text: PDF file (226 kB)
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UDC: 517.54+517.862
Received: 18.05.2010
Received in revised form: 25.06.2010
Accepted: 10.07.2010

Citation: Olga A. Sergeeva, “The bilinear pairings for the holomorphic $(q,\rho)$-forms”, J. Sib. Fed. Univ. Math. Phys., 4:1 (2011), 128–139

Citation in format AMSBIB
\Bibitem{Ser11}
\by Olga~A.~Sergeeva
\paper The bilinear pairings for the holomorphic $(q,\rho)$-forms
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2011
\vol 4
\issue 1
\pages 128--139
\mathnet{http://mi.mathnet.ru/jsfu170}


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    This publication is cited in the following articles:
    1. O. A. Sergeeva, “The Poincare Series and Operators of Duality for Multiplicative Automorphic Forms”, J. Math. Sci., 205:3 (2015), 445–454  mathnet  crossref
  • Журнал Сибирского федерального университета. Серия "Математика и физика"
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