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Article: Locally harmonic Maass forms and the kernel of the Shintani lift
Title | Locally harmonic Maass forms and the kernel of the Shintani lift |
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Authors | |
Issue Date | 2015 |
Citation | International Mathematical Research Notices (In press), 2015 How to Cite? |
Abstract | In 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 Identifier | http://hdl.handle.net/10722/199118 |
ISSN | 2023 Impact Factor: 0.9 2023 SCImago Journal Rankings: 1.337 |
ISI Accession Number ID |
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Bringmann, K | en_US |
dc.contributor.author | Kohnen, W | en_US |
dc.contributor.author | Kane, BR | en_US |
dc.date.accessioned | 2014-07-22T01:03:53Z | - |
dc.date.available | 2014-07-22T01:03:53Z | - |
dc.date.issued | 2015 | - |
dc.identifier.citation | International Mathematical Research Notices (In press), 2015 | en_US |
dc.identifier.issn | 1073-7928 | - |
dc.identifier.uri | http://hdl.handle.net/10722/199118 | - |
dc.description.abstract | In 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.language | eng | en_US |
dc.relation.ispartof | International Mathematical Research Notices | en_US |
dc.title | Locally harmonic Maass forms and the kernel of the Shintani lift | en_US |
dc.type | Article | en_US |
dc.identifier.email | Kane, BR: bkane@hku.hk | en_US |
dc.identifier.authority | Kane, BR=rp01820 | en_US |
dc.description.nature | postprint | - |
dc.identifier.doi | 10.1093/imrn/rnu024 | en_US |
dc.identifier.scopus | eid_2-s2.0-84941903410 | - |
dc.identifier.hkuros | 230759 | en_US |
dc.identifier.eissn | 1687-0247 | - |
dc.identifier.isi | WOS:000356707200009 | - |
dc.identifier.issnl | 1073-7928 | - |