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Sibirsk. Mat. Zh., 2015, Volume 56, Number 3, Pages 693–703 (Mi smj2670)  

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.

DOI: https://doi.org/10.17377/smzh.2015.56.318

Full text: PDF file (314 kB)
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English version:
Siberian Mathematical Journal, 2015, 56:3, 549–556

Bibliographic databases:

UDC: 515.17+517.545
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

Citation in format AMSBIB
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