Experimental L-functions

An L-function is a Dirichlet series which has an Euler
product, analytic continuation and functional equation of appropriate
type. I will present numerical methods which allow, with reasonable
confidence, to find all L-functions of given type. The method is
applied to find L-functions which should correspond to Calabi-Yau
threefolds with h12=1 on the motivic side and to paramodular cusp
forms of weight 3 on the automorphic side.