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dc.contributor.authorBruggeman, Roelof W.
dc.contributor.authorCh'oe, Yŏng-ju
dc.contributor.authorDiamantis, Nikolaos
dc.date.accessioned2014-04-25T12:00:02Z
dc.date.accessioned2016-10-05T14:13:58Z
dc.date.available2014-04-25T12:00:02Z
dc.date.available2016-10-05T14:13:58Z
dc.date.issued2014-04-25
dc.identifier.urihttp://publications.mfo.de/handle/mfo/1078
dc.descriptionResearch in Pairs 2014en_US
dc.description.abstractWe 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. We use Knopp’s generalization of this integral to real weights, and apply it to complex weights that are not an integer at least 2. We 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. We impose no condition on the growth of the automorphic forms at the cusps. So our result covers exponentially growing automorphic forms, like those studied by Borcherds, and like those in the theory of mock automorphic forms. For real weights that are not an integer at least 2 we similarly characterize the space of cusp forms and the space of entire automorphic forms. We give a relation between the cohomology classes attached to holomorphic automorphic forms of real weight and the existence of harmonic lifts. A tool in establishing these results is the relation to cohomology groups with values in modules of “analytic boundary germs”, which are represented by harmonic functions on subsets of the upper half-plane. It turns out that for integral weights at least 2 the map from general holomorphic automorphic forms to cohomology with values in analytic boundary germs is injective. So cohomology with these coefficients can distinguish all holomorphic automorphic forms, unlike the classical Eichler theory.en_US
dc.language.isoenen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2014,07
dc.subjectHolomorphic automorphic formen_US
dc.subjectEichler integralen_US
dc.subjectCohomologyen_US
dc.subjectMixed parabolic cohomologyen_US
dc.subjectPeriod functionen_US
dc.subjectHarmonic liften_US
dc.subjectHarmonic functionsen_US
dc.subjectBoundary germen_US
dc.titleHolomorphic automorphic forms and cohomologyen_US
dc.typePreprinten_US
dc.identifier.doi10.14760/OWP-2014-07
local.scientificprogramResearch in Pairs 2014
local.series.idOWP-2014-07
local.subject.msc11
local.subject.msc22


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