Periods of mixed automorphic forms and differential equations (Q1808631)

The purpose of this paper is to establish certain relations between the periods of mixed automorphic forms, i.e., a generalization of ordinary automorphic forms, and the monodromy of differential equations associated with them. The author of this paper constructs a solution of a differential equation associated with a mixed automorphic form using the mixed automorphic form and conversely makes a mixed automorphic form from a solution to an ordinary differential equation. Then he writes a cocycle in the cohomology group of the monodromy associated to solutions of ordinary differential equations by using the periods of mixed automorphic forms.