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Journal of Siberian Federal University. Mathematics & Physics, 2013, Volume 6, Issue 2, Pages 200–210 (Mi jsfu308)  
The Newton polytope of the optimal differential operator for an algebraic curve

Vitaly A. Krasikova, Timur M. Sadykovb

a Institute of Mathematics and Computer Science, Siberian Federal University, Krasnoyarsk, Russia
b Department of Information Technologies, Russian State University of Trade and Economics, Moscow, Russia
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Abstract: We investigate the linear differential operator with polynomial coefficients whose space of holomorphic solutions is spanned by all the branches of a function defined by a generic algebraic curve. The main result is a description of the coefficients of this operator in terms of their Newton polytopes.
Keywords: algebraic function, minimal differential operator, Newton polytope.
Received: 30.12.2012
Received in revised form: 10.01.2013
Accepted: 25.02.2013
Document Type: Article
UDC: 510.52+517.554+517.953
Language: English
Citation: Vitaly A. Krasikov, Timur M. Sadykov, “The Newton polytope of the optimal differential operator for an algebraic curve”, J. Sib. Fed. Univ. Math. Phys., 6:2 (2013), 200–210
Citation in format AMSBIB
\Bibitem{KraSad13}
\by Vitaly~A.~Krasikov, Timur~M.~Sadykov
\paper The Newton polytope of the optimal differential operator for an algebraic curve
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2013
\vol 6
\issue 2
\pages 200--210
\mathnet{http://mi.mathnet.ru/jsfu308}
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    		Журнал Сибирского федерального университета. Серия "Математика и физика"
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