Linear differential operators for generic algebraic curves

2010/01/15 by V. A. Krasikov, Krasikov, V. A., Timur Sadykov +2 · 1 citation
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Algebraic and Geometric Analysis #Polynomial and algebraic computation #math.AP #math.CA #msc:34M50 #msc:35N10

paper · pdf · doi:10.48550/arxiv.1001.2607

arxiv created 2010/01/15 · arxiv updated 2010/02/26

Abstract

We give a computationally efficient method for constructing 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 proposed method does not require solving the algebraic equation and can be applied in the case when its Galois group is not solvable.

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