Holomorphic automorphic forms and cohomology
著者
書誌事項
Holomorphic automorphic forms and cohomology
（Memoirs of the American Mathematical Society, no. 1212）
American Mathematical Society, c2018
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注記
Includes bibliographical references and indexes
May 2018, volume 253, number 1212 (seventh of 7 numbers)
内容説明・目次
内容説明
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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