Abstract
The theory of multiplicative functions and Prym differentials on a compact Riemann surface has found numerous applications in function theory, analytic number theory, and equations of mathematical physics. We give a full constructive description for the divisors of elementary abelian differentials of integer order and all three kinds depending holomorphically on the modulus of compact Riemann surfaces F. We study the location of zeros of holomorphic Prym differentials on F, as well as the structure of the set of (multiplicatively) special divisors on F in the spaces Fg−1 and Fg−2.
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