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 J. Sib. Fed. Univ. Math. Phys., 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

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.

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UDC: 510.52+517.554+517.953
Accepted: 25.02.2013
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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}