Geodesic
Multiplicative Functions with Matrix Characters on Compact Riemann Surfaces
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 2 (2009) no. 1, pp. 31-40

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The theory of multiplicative functions and Prym differentials for special (scalar) characters on compact Riemann surfaces has many applications in the theory of functions, in analytic numbers theory and in mathematical physics. In this article we proove existence of matrix multiplicative functions and Prym $m$-differentials for every matrix characters with values in $GL(n;\mathbb C)$ on compact Riemann surfaces.
Keywords: compact Riemann surface, multiplicative functions and Prym differentials, matrix characters, theta Poincaré series, Fuchsian group. 
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     author = {Alena A. Bespomestnych and Victor V. Chueshev},
     title = {Multiplicative {Functions} with {Matrix} {Characters} on {Compact} {Riemann} {Surfaces}},
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Alena A. Bespomestnych; Victor V. Chueshev. Multiplicative Functions with Matrix Characters on Compact Riemann Surfaces. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 2 (2009) no. 1, pp. 31-40. http://geodesic.mathdoc.fr/item/JSFU_2009_2_1_a2/