Why does the WF being in the lowest landau level entail that f(z) must be analyt...

[github-actions]

https://github.com/ThomasFKJorna/thesis-writing/blob/e51023451325d184f4235d26fef02820334084ef/Chapters/III. Anyons/4. The Quantum Hall Effect.md#L248

1) we do try to generalize, and say that a wavefunction for n particles will look something like $f(z)e^{something}$
2) we _insist_ that the wavefunction be in the lowest landau level (lll) it can possibly be: there are no other landau levels it can fall back on.

{/**
    * TODO: Why does the WF being in the lowest landau level entail that f(z) must be analytic?
    * labels: expansion
  */}

         this is rather strong. This leads to the claim that $f(z)$ _must_ be analytic.