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Article: Locally harmonic Maass forms and the kernel of the Shintani lift

TitleLocally harmonic Maass forms and the kernel of the Shintani lift
Authors
Issue Date2015
Citation
International Mathematical Research Notices (In press), 2015 How to Cite?
AbstractIn this paper we define a new type of modular object and construct explicit examples of such functions. Our functions are closely related to cusp forms constructed by Zagier which played an important role in the construction by Kohnen and Zagier of a kernel function for the Shimura and Shintani lifts between half-integral and integral weight cusp forms. Although our functions share many properties in common with harmonic weak Maass forms, they also have some properties which strikingly contrast those exhibited by harmonic weak Maass forms. As a first application of the new theory developed in this paper, one obtains a new perspective on the fact that the even periods of Zagier's cusp forms are rational as an easy corollary.
Persistent Identifierhttp://hdl.handle.net/10722/199118

 

DC FieldValueLanguage
dc.contributor.authorBringmann, Ken_US
dc.contributor.authorKohnen, Wen_US
dc.contributor.authorKane, BRen_US
dc.date.accessioned2014-07-22T01:03:53Z-
dc.date.available2014-07-22T01:03:53Z-
dc.date.issued2015-
dc.identifier.citationInternational Mathematical Research Notices (In press), 2015en_US
dc.identifier.urihttp://hdl.handle.net/10722/199118-
dc.description.abstractIn this paper we define a new type of modular object and construct explicit examples of such functions. Our functions are closely related to cusp forms constructed by Zagier which played an important role in the construction by Kohnen and Zagier of a kernel function for the Shimura and Shintani lifts between half-integral and integral weight cusp forms. Although our functions share many properties in common with harmonic weak Maass forms, they also have some properties which strikingly contrast those exhibited by harmonic weak Maass forms. As a first application of the new theory developed in this paper, one obtains a new perspective on the fact that the even periods of Zagier's cusp forms are rational as an easy corollary.en_US
dc.languageengen_US
dc.relation.ispartofInternational Mathematical Research Noticesen_US
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.titleLocally harmonic Maass forms and the kernel of the Shintani liften_US
dc.typeArticleen_US
dc.identifier.emailKane, BR: bkane@hku.hken_US
dc.identifier.authorityKane, BR=rp01820en_US
dc.description.naturepostprint-
dc.identifier.doi10.1093/imrn/rnu024en_US
dc.identifier.hkuros230759en_US

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