Holomorphic Automorphic Forms and Cohomology 1

Vetenskap & teknik

Holomorphic Automorphic Forms and Cohomology

Roelof Bruggeman • Youngju Choie • Nikolaos Diamantis

Pocket

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159 sidor
2018

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.

Författare: Roelof Bruggeman, Youngju Choie, Nikolaos Diamantis
Format: Pocket/Paperback
ISBN: 9781470428556
Språk: Engelska
Antal sidor: 159
Utgivningsdatum: 2018-06-30
Förlag: American Mathematical Society