Abstract
The problem of finding and calculating numerically a conformal mapping which simultaneously uniformizes several branch points in energy of a partial wave scattering amplitude is studied. Arguing from a potential scattering model a general prescription is given for the construction of such conformal mappings in terms of automorphic forms. The automorphic forms are defined with respect to a group each of whose generators arises from one of the cuts in the energy plane of the scattering amplitude. The automorphic forms are calculated numerically from their Fourier series. The method is illustrated in detail for a relativistic single particle exchange model. Finally it is shown how the conformal mapping leads to simple representations of the analytic properties of the amplitude in terms of the uniformizing variable.