
Holomorphic Automorphic Forms and Cohomology
American Mathematical Society (Publisher)
Will be published approx. on 30. June 2018
Book
Paperback/Softback
159 pages
978-1-4704-2855-6 (ISBN)
Description
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.
More details
Series
Language
English
Place of publication
Providence
United States
Target group
Professional and scholarly
Dimensions
Height: 254 mm
Width: 178 mm
Weight
272 gr
ISBN-13
978-1-4704-2855-6 (9781470428556)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Persons
Roelof Bruggeman, Universiteit Utrecht, The Netherlands.
Youngju Choie, Pohang University of Science and Technology, South Korea.
Nikolaos Diamantis, University of Nottingham, United Kingdom.
Youngju Choie, Pohang University of Science and Technology, South Korea.
Nikolaos Diamantis, University of Nottingham, United Kingdom.