On Special monodromy groups and Riemann-Hilbert problem for Riemann equation

2004/12/06 by V. Poberezhny, Poberezhny, V.
Mathematics · #34m45 #34m50 #Algebraic Geometry (math.AG) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.AG #math.CA #msc:34m45 #msc:34m50

paper · pdf · doi:10.48550/arxiv.math/0412115

18 pages, to appear in Math. Notes

arxiv created 2004/12/22 · arxiv updated 2009/12/01

Abstract

In the present work we use the Levelt's valuation theory to describe all monodromy representations that can be realized by Riemann equation. Also we show that if the monodromy of Riemann equation lies in SL(2,ℂ), then such a monodromy can be realized by a more special Riemann-Sturm-Liouville equation as well. After all the criterion for hypergeometric equation to have monodromy in SL(2,ℤ) is presented.

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