The Riemann Hypothesis and Holomorphic Index in Complex Dynamics

We present an interpretation of the Riemann hypothesis in terms of complex and topological dynamics. For example, the Riemann hypothesis is true and all zeros of the Riemann zeta function are simple if and only if a meromorphic function that is explicitly given in this note has no attracting fixed point. To obtain this, we use the holomorphic index (residue fixed point index) that characterizes the local properties of the fixed points in complex dynamics.