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Siberian Mathematical Journal

, Volume 56, Issue 3, pp 549–556 | Cite as

Prym differentials with matrix characters on a finite Riemann surface

  • O. A. ChueshevaEmail author
Article
  • 23 Downloads

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,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 

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Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.Kemerovo State UniversityKemerovoRussia

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