  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.

Classical Analysis and ODEs;Algebraic Geometry