Geodesic
The bilinear pairings for the holomorphic $(q,\rho)$-forms
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 4 (2011) no. 1, pp. 128-139

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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. 
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     author = {Olga A. Sergeeva},
     title = {The bilinear pairings for the holomorphic $(q,\rho)$-forms},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {128--139},
     publisher = {mathdoc},
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     number = {1},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2011_4_1_a14/}
}
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Olga A. Sergeeva. The bilinear pairings for the holomorphic $(q,\rho)$-forms. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 4 (2011) no. 1, pp. 128-139. http://geodesic.mathdoc.fr/item/JSFU_2011_4_1_a14/