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Russian Mathematical Surveys, 2004, Volume 59, Issue 6, Pages 1117–1154
DOI: https://doi.org/10.1070/RM2004v059n06ABEH000798 (Mi rm798) 		 
This article is cited in 17 scientific papers (total in 17 papers)

Analytic theory of difference equations with rational and elliptic coefficients and the Riemann–Hilbert problem

I. M. Kricheverab

a L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences
b Columbia University
English version PDF (409 kB) Citations (17)
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DOI: https://doi.org/10.1070/RM2004v059n06ABEH000798
Abstract: A new approach to the construction of the analytic theory of difference equations with rational and elliptic coefficients is proposed, based on the construction of canonical meromorphic solutions which are analytic along “thick” paths. The concept of these solutions leads to the definition of local monodromies of difference equations. It is shown that, in the continuous limit, these local monodromies converge to monodromy matrices of differential equations. In the elliptic case a new type of isomonodromy transformations changing the periods of elliptic curves is constructed.
Received: 28.06.2004
Russian version:
Uspekhi Matematicheskikh Nauk, 2004, Volume 59, Issue 6(360), Pages 111–150
DOI: https://doi.org/10.4213/rm798
Bibliographic databases:
Document Type: Article
UDC: 517.9
MSC: Primary 30E25, 39A11, 34M35; Secondary 34M50, 34M55, 45E05, 30D99, 32S40, 14H52
Language: English
Original paper language: Russian
Citation: I. M. Krichever, “Analytic theory of difference equations with rational and elliptic coefficients and the Riemann–Hilbert problem”, Uspekhi Mat. Nauk, 59:6(360) (2004), 111–150; Russian Math. Surveys, 59:6 (2004), 1117–1154
Citation in format AMSBIB
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    • This publication is cited in the following 17 articles:
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    References:101
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