Commensurabilities among Lattices in PU (1,n)

The first part of this monograph is devoted to a characterization of hypergeometric-like functions, that is, twists of hypergeometric functions in n -variables. These are treated as an ( n +1) dimensional vector space of multivalued locally holomorphic functions defined on the space of n +3 tuples of distinct points on the projective line P modulo, the diagonal section of Auto P = m . For n =1, the characterization may be regarded as a generalization of Riemann's classical theorem characterizing