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Single-valued differentials and special divisors of Prym differentials

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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 F g−1 and F g−2.

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Authors and Affiliations

  1. Gorno-Altaĭsk State University, Gorno-Altaĭsk, Russia

    M. I. Tulina

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  1. M. I. Tulina
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Correspondence to M. I. Tulina.

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Original Russian Text Copyright © 2013 Tulina M.I.

The author was supported by the Russian Foundation for Basic Research (Grant 11-01-90709), the Program “Development of the Scientific Potential of Higher School” of the Russian Federal Agency for Education (Grant 2.1.1.3707), and the Special Federal Program (Grant 02.740.11.0457).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 54, No. 4, pp. 914–931, July–August, 2013.

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Tulina, M.I. Single-valued differentials and special divisors of Prym differentials. Sib Math J 54, 731–745 (2013). https://doi.org/10.1134/S0037446613040137

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  • DOI: https://doi.org/10.1134/S0037446613040137

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