Prym differentials with matrix characters on a finite Riemann surface
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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.
KeywordsPrym differential for a matrix character finite Riemann surface Poincaré theta-series
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