i’m very new in Mathematica. I want to solve the Bethe Ansatz Equations for the so-called “Hofstadter-Problem”. These are equations in the Form like:

$ $ z^2_{l}=q^{Q}*\prod^{Q-1}_{m\neq l}\frac{q^2*z_{l}-z_{m}}{z_{l}-q^2*z_{m}}$ $

for $ $ l=1,…,Q-1$ $ , $ q$ is just a complex number $ $ q=e^{i \pi \frac{P}{Q}}$ $ , and Q is an integer.

So i want to solve this equations for $ Q=1,2,3,\ldots$ , $ \frac{P}{Q}$ ist the magnetic flux.

Does anyone has some ideas? Please, i really need some help.

Thanks a lot in advance.

Q = 2, 3, 4, ....u0 =    Do[FindRoot[     Subscript[z, l]^2 ==       q^Q*Product[(q^2 Subscript[z, l] - Subscript[z, m])/(Subscript[z,            l] - q^2 Subscript[z, m]), {m, 1, Q - 1}],      WorkingPrecision -> 50, AccuracyGoal -> 20];     ListPlot[Transpose[{u0 // Re, u0 // Im}], PlotRange -> All,      AspectRatio -> Automatic]