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Finite-gap solutions of the Fuchsian equation

Alexander O. Smirnov
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Abstract

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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Alexander O. Smirnov. 2003-10-29. Finite-gap solutions of the Fuchsian equation. https://arxiv.org/abs/math/0310465

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