Holomorphic Automorphic Forms and Cohomology
Roelof Bruggeman author Youngju Choie author Nikolaos Diamantis author
Format:Paperback
Publisher:American Mathematical Society
Published:30th Jun '18
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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.
ISBN: 9781470428556
Dimensions: unknown
Weight: 272g
159 pages