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Holomorphic Automorphic Forms and Cohomology

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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.
Request Code : ZLIBIO3922978
Categories:
Year:
2018
Edition:
1
Publisher:
American Mathematical Society
Language:
English
Pages:
182
ISBN 13:
9781470428556
ISBN:
9781470444198,9781470428556
Series:
Memoirs of the American Mathematical Society Ser.

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