On Gustav Doetch's Introduction to the Theory and Application of the Laplace Transform, it says:
The power series $\sum_{n=0}^\infty a_nz^n$ converges on a circular disc. Replacing the integers $n$ by real-valued $\lambda_n$ we have to consider the multivalued behaviour of $z^{\lambda_n}$. Accordingly, the circular disc of convergence is to be envisaged as a portion of a multi-layered Riemann surface.
I think I got why $z^{\lambda_n}$ is multivalued: $\mathcal{z}^x$ exponential is defined as $e^{x\log(z)}$, so if $x$ is a integer, then this exponential doesn't depend on the choice of $\log(z)$, but if it's real, those different logs will give different results. My question is, what is "a portion of a multi-layered Riemann surface" is this case?