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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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/

[1] O. A. Sergeeva, “Banakhovy prostranstva multiplikativnykh avtomorfnykh form”, Vestnik NGU, 5:4 (2005), 45–63

[2] O. A. Sergeeva, “Modifitsirovannye operatory Bersa i dvoistvennost golomorfnykh multiplikativnykh avtomorfnykh form”, Sib. matem. zhurn., 50:4 (2009), 902–914 | MR

[3] H. M. Farkas, I. Kra, Riemann Surfaces, Graduate Texts in Mathematics, 71, Springer-Verlag, 1992 | MR | Zbl

[4] L. Bers, “A non-standard integral equation with applications to quasiconformal mappings”, Acta Math., 116 (1966), 115–134 | DOI | MR

[5] I. Kra, Avtomorfnye formy i kleinovy gruppy, Mir, M., 1975 | MR | Zbl

[6] V. V. Chueshev, Multiplikativnye funktsii i differentsialy Prima na peremennoi kompaktnoi rimanovoi poverkhnosti, Ch. 2, KemGU, Kemerovo, 2003 | Zbl