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

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

2004-12-06

arxiv.org/abs/math/0412115v2

Mathematics

Classical Analysis and ODEs

18 pages, to appear in Math. Notes

Scientific paper

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 $SL(2,\mathbb{C})$, 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 $SL(2,\mathbb{Z})$ is presented.

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