Geodesic
The Newton polytope of the optimal differential operator for an algebraic curve
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 6 (2013) no. 2, pp. 200-210

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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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Vitaly A. Krasikov; Timur M. Sadykov. The Newton polytope of the optimal differential operator for an algebraic curve. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 6 (2013) no. 2, pp. 200-210. http://geodesic.mathdoc.fr/item/JSFU_2013_6_2_a6/