Finite-gap solutions of the Fuchsian equation

Alexander O. Smirnov

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Finite-gap solutions of the Fuchsian equation

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arxiv math/0310465 v2 pith:XYMS77W2 submitted 2003-10-29 math.CA math-phmath.MPmath.SP

Alexander O. Smirnov This is my paper · ORCID

classification math.CAmath-phmath.MPmath.SP

keywords algebraiccurvefuchsiansolutionsbelongingbranchingcalculatingclass

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We find a new class of the Fuchsian equations, which have an algebraic geometric solutions with the parameter belonging to a hyperelliptic curve. Methods of calculating the algebraic genus of the curve, and its branching points, are suggested. Numerous examples are given.

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