Holomorphic Automorphic Forms and Cohomology - Bruggeman, Roelof; Choie, YoungJu; Diamantis, Nikolaos (Memoirs of the American Mathematical Society, 2018)
We investigate the correspondence between holomorphic automorphic forms on the upper half-plane with complex weight and parabolic cocycles. For integral weights at least For real weights that are not an integer at least A tool in establishing these results is the relation to cohomology groups with values in modules of “analytic boundary germs”, which are represented by harmonic functions on subsets of the upper half-plane. It turns out that for integral weights at least