Holomorphic automorphic forms and cohomology

Roelof W. Bruggeman, Yŏng-Ju Ch'oe & Nikolaos Diamantis
We investigate the correspondence between holomorphic automorphic forms on the upper half-plane with complex weight and parabolic cocycles. For integral weights at least 2 this correspondence is given by the Eichler integral. We use Knopp’s generalization of this integral to real weights, and apply it to complex weights that are not an integer at least 2. We show that for these weights the generalized Eichler integral gives an injection into the first cohomology group with...
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