Holomorphic Automorphic Forms and Cohomology 1st Edition by Roelof Bruggeman; Youngju Choie; Nikolaos Diamantis 1470444194 9781470444198

Holomorphic Automorphic Forms and Cohomology 1st Edition Roelof Bruggeman – Ebook Instant Download/Delivery ISBN(s): 9781470444198,1470444194

Product details:

• ISBN 10:1470444194
• ISBN 13:9781470444198
• Author:Roelof Bruggeman; Youngju Choie; Nikolaos Diamantis

The authors 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. The authors use Knopp’s generalization of this integral to real weights, and apply it to complex weights that are not an integer at least $2$. They show that for these weights the generalized Eichler integral gives an injection into the first cohomology group with values in a module of holomorphic functions, and characterize the image. The authors impose no condition on the growth of the automorphic forms at the cusps. Their result concerns arbitrary cofinite discrete groups with cusps, and covers exponentially growing automorphic forms, like those studied by Borcherds, and like those in the theory of mock automorphic forms.

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