Finite-gap solutions of the Fuchsian equation

2003/10/29 by Alexander O. Smirnov, Smirnov, Alexander O.
Mathematics · Physics and Astronomy · #14H70 (Secondary) #33E30 (Primary) #34L40 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP) #math-ph #math.CA #math.MP #math.SP #msc:14H70 #msc:33E30 #msc:34L40

paper · pdf · doi:10.48550/arxiv.math/0310465

19 pages, LaTeX2e (AMSLaTeX)

arxiv created 2003/10/29 · arxiv updated 2009/12/01

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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