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Prym Differentials on Variable Tori

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We consider multiplicative functions and Prym differentials on variable tori. We prove counterparts of the theorem on the total sum of residues for Prym differentials of any integer order on tori. As a consequence, reciprocity laws are proved. We construct elementary Prym differentials of all kinds with any integer order which holomorphically depend on the moduli of tori and characters. We derive an analogue of the Appell decomposition formula for functions with characters. We also study vector bundles of Prym differentials of any integer order over the product of Teichmueller spaces for a torus and a group of characters.

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Authors and Affiliations

  1. Kemerovo State University, 6, Krasnaya St., Kemerovo, 650043, Russia

    T. S. Krepitsina & V. V. Chueshev

Authors
  1. T. S. Krepitsina
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  2. V. V. Chueshev
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Correspondence to V. V. Chueshev.

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Translated from Sibirskii Zhurnal Chistoi i Prikladnoi Matematiki 16, No. 3, 2016, pp. 40-54.

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Krepitsina, T.S., Chueshev, V.V. Prym Differentials on Variable Tori. J Math Sci 230, 79–94 (2018). https://doi.org/10.1007/s10958-018-3729-9

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  • DOI: https://doi.org/10.1007/s10958-018-3729-9

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