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Bringmann, Kathrin; Diamantis, Nikolaos; Raum, Martin (2013)
Publisher: Elsevier
Journal: Advances in Mathematics
Languages: English
Types: Article
Subjects: Mathematics(all), Mathematics - Number Theory, 11F67, 11F03

Classified by OpenAIRE into

arxiv: Mathematics::Number Theory
We introduce a new technique of completion for 1-cohomology which parallels the corresponding technique in the theory of mock modular forms. This technique is applied in the context of non-critical values of L-functions of GL(2) cusp forms. We prove that a generating series of non-critical values can be interpreted as a mock period function we\ud define in analogy with period polynomials. Further, we prove that non-critical values can be encoded into a sesquiharmonic Maass form. Finally, we formulate and prove an Eichler-Shimura-type isomorphism for the space of mock period functions.
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