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Mat. Zametki, 2017, Volume 101, Issue 1, Pages 91–100 (Mi mz11107)  

This article is cited in 1 scientific paper (total in 1 paper)

The One-Dimensional Riemann Problem on an Elliptic Curve

A. A. Matveevaa, V. A. Poberezhnyiab

a National Research University "Higher School of Economics" (HSE), Moscow
b State Scientific Center of the Russian Federation - Institute for Theoretical and Experimental Physics, Moscow

Abstract: A one-dimensional generalization of the Riemann–Hilbert problem from the Riemann sphere to an elliptic curve is considered. A criterion for its positive solvability is obtained and the explicit form of all possible solutions is found. As in the spherical case, the solutions turn out to be isomonodromic.

Keywords: Riemann problem, elliptic curve, logarithmic connection.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-11-10160
14-01-00547
Ministry of Education and Science of the Russian Federation


DOI: https://doi.org/10.4213/mzm11107

Full text: PDF file (433 kB)
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English version:
Mathematical Notes, 2017, 101:1, 115–122

Bibliographic databases:

Document Type: Article
UDC: 517.925.7
PACS: 02.30.Zz
Received: 26.06.2016
Revised: 09.08.2016

Citation: A. A. Matveeva, V. A. Poberezhnyi, “The One-Dimensional Riemann Problem on an Elliptic Curve”, Mat. Zametki, 101:1 (2017), 91–100; Math. Notes, 101:1 (2017), 115–122

Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm11107
  • http://mi.mathnet.ru/eng/mz/v101/i1/p91

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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. A. A. Matveeva, V. A. Poberezhny, “Two-dimensional Riemann problem for rigid representations on an elliptic curve”, J. Geom. Phys., 114 (2017), 384–393  crossref  mathscinet  zmath  isi  scopus
  • Математические заметки Mathematical Notes
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