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Prym differentials with matrix characters on a finite Riemann surface
O. A. Chueshevaab a Kemerovo State University, Kemerovo, Russia
b Siberian Federal University, Krasnoyarsk, Russia
Abstract:
The theory of multiplicative functions and Prym differentials for scalar characters on a compact Riemann surface has found applications in function theory, analytic number theory, and mathematical physics.
We construct the matrix multiplicative functions and Prym $m$-differentials on a finite Riemann surface for a given matrix character with values in $GL(n,\mathbb C)$ starting from a meromorphic function on the unit disk with finitely many poles. We show that these multiplicative functions and Prym $m$-differentials depend locally holomorphically on the matrix character.
Keywords:
Prym differential for a matrix character, finite Riemann surface, Poincaré theta-series.
Received: 22.04.2014 Revised: 15.12.2014
Citation:
O. A. Chuesheva, “Prym differentials with matrix characters on a finite Riemann surface”, Sibirsk. Mat. Zh., 56:3 (2015), 693–703; Siberian Math. J., 56:3 (2015), 549–556
Linking options:
https://www.mathnet.ru/eng/smj2670 https://www.mathnet.ru/eng/smj/v56/i3/p693
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