Vitaly A. Krasikov, Timur M. Sadykov, “The Newton polytope of the optimal differential operator for an algebraic curve”, J. Sib. Fed. Univ. Math. Phys., 2013, Volume 6, Issue 2,Pages <nobr>200

The Newton polytope of the optimal differential operator for an algebraic curve

Vitaly A. Krasikov^a, Timur M. Sadykov^b

^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.

UDC: 510.52+517.554+517.953

Received: 30.12.2012
Received in revised form: 10.01.2013
Accepted: 25.02.2013

Language: English