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 SIGMA, 2012, Volume 8, 044, 11 pages (Mi sigma721)

Commuting differential operators of rank 3 associated to a curve of genus 2

Dafeng Zuoab

a School of Mathematical Science, University of Science and Technology of China, Hefei 230026, P.R. China
b Wu Wen-Tsun Key Laboratory of Mathematics, USTC, Chinese Academy of Sciences, P.R. China

Abstract: In this paper, we construct some examples of commuting differential operators $L_1$ and $L_2$ with rational coefficients of rank 3 corresponding to a curve of genus 2.

Keywords: commuting differential operators, rank 3, genus 2.

DOI: https://doi.org/10.3842/SIGMA.2012.044

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Bibliographic databases:

ArXiv: 1105.5774
MSC: 13N10; 14H45; 34L99; 37K20
Received: March 12, 2012; in final form July 12, 2012; Published online July 15, 2012
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Citation: Dafeng Zuo, “Commuting differential operators of rank 3 associated to a curve of genus 2”, SIGMA, 8 (2012), 044, 11 pp.

Citation in format AMSBIB
\Bibitem{Zuo12} \by Dafeng Zuo \paper Commuting differential operators of rank~3 associated to a curve of genus~2 \jour SIGMA \yr 2012 \vol 8 \papernumber 044 \totalpages 11 \mathnet{http://mi.mathnet.ru/sigma721} \crossref{https://doi.org/10.3842/SIGMA.2012.044} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2958986} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000306353300001} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84864834320} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. V. N. Davletshina, “O samosopryazhennykh kommutiruyuschikh differentsialnykh operatorakh ranga dva”, Sib. elektron. matem. izv., 10 (2013), 109–112
2. V. N. Davletshina, E. I. Shamaev, “On commuting differential operators of rank $2$”, Siberian Math. J., 55:4 (2014), 606–610
3. Mironov A.E., “Self-Adjoint Commuting Ordinary Differential Operators”, Invent. Math., 197:2 (2014), 417–431
4. V. N. Davletshina, “Self-Adjoint Commuting Differential Operators of Rank 2 and Their Deformations Given by Soliton Equations”, Math. Notes, 97:3 (2015), 333–340
5. V. N. Davletshina, “Commuting differential operators of rank $2$ with trigonometric coefficients”, Siberian Math. J., 56:3 (2015), 405–410
6. Zheglov A.B., Mironov A.E., “on Commuting Differential Operators With Polynomial Coefficients Corresponding To Spectral Curves of Genus One”, Dokl. Math., 91:3 (2015), 281–282
7. A. E. Mironov, “Self-adjoint commuting differential operators of rank two”, Russian Math. Surveys, 71:4 (2016), 751–779
8. A. B. Zheglov, A. E. Mironov, B. T. Saparbayeva, “Commuting Krichever–Novikov differential operators with polynomial coefficients”, Siberian Math. J., 57:5 (2016), 819–823
9. Mironov A.E., Zheglov A.B., “Commuting Ordinary Differential Operators with Polynomial Coefficients and Automorphisms of the First Weyl Algebra”, Int. Math. Res. Notices, 2016, no. 10, 2974–2993
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