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 Sibirsk. Mat. Zh., 2016, Volume 57, Number 1, Pages 157–170 (Mi smj2735)

Prym differentials as solutions to boundary value problems on Riemann surfaces

E. V. Semenko

Novosibirsk State University, Novosibirsk, Russia

Abstract: Construction of multiplicative functions and Prym differentials, including the case of characters with branch points, reduces to solving a homogeneous boundary value problem on the Riemann surface. The use of the well-established theory of boundary value problems creates additional possibilities for studying Prym differentials and related bundles. Basing on the theory of boundary value problems, we fully describe the class of divisors of Prym differentials and obtain new integral expressions for Prym differentials, which enable us to study them directly and, in particular, to study their dependence on the point of the Teichmüller space and characters. Relying on this, we obtain and generalize certain available results on Prym differentials by a new method.

Keywords: Riemann surface, multiplicative function, Prym differential, homogeneous boundary value problem.

DOI: https://doi.org/10.17377/smzh.2016.57.112

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English version:
Siberian Mathematical Journal, 2016, 57:1, 124–134

Bibliographic databases:

UDC: 517.53/55

Citation: E. V. Semenko, “Prym differentials as solutions to boundary value problems on Riemann surfaces”, Sibirsk. Mat. Zh., 57:1 (2016), 157–170; Siberian Math. J., 57:1 (2016), 124–134

Citation in format AMSBIB
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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. E. V. Semenko, “Connection between holomorphic vector bundles and cohomology on a Riemann surface and conjugation boundary value problems”, Siberian Math. J., 58:2 (2017), 310–318
2. E. V. Semenko, “Reduction of vector boundary value problems on Riemann surfaces to one-dimensional problems”, Siberian Math. J., 60:1 (2019), 153–163
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