
The Lam\'{e} differential equation $L_n(y)=0$ is the second order linear differential equationAlexa van der Waall, University of Utrecht
The Lam\'{e} differential equation $L_n(y)=0$ is the second order linear differential equation $p(z)y''(z)+{1/2}p'(z)y'(z)(n(n+1)+B)y(z)=0$ for a certain polynomial $p(z)$ of degree $3$ in $z$ and constants $n$ and $B$. There exist cases in which the solution space of the Lam\'{e} equation only consists of algebraic solutions. A number of qualitative results on this subject have been given by F. Baldassari and B. Chiarellotto. Some of their results will be mentioned in this talk. The exploration of the notion of a monodromy group yields some explicit algorithms for the construction of the Lame\'{e} equations with only algebraic solutions. We shall descibe at least one of these algorithms and show how it works. 