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Article: Shintani lifts and fractional derivatives for harmonic weak Maass forms

TitleShintani lifts and fractional derivatives for harmonic weak Maass forms
Authors
Issue Date2014
PublisherElsevier. The Journal's web site is located at http://www.elsevier.com/locate/aim
Citation
Advances in Mathematics, 2014, v. 255, p. 641-671 How to Cite?
AbstractIn this paper, we construct Shintani lifts from integral weight weakly holomorphic modular forms to half-integral weight weakly holomorphic modular forms. Although defined by different methods, these coincide with the classical Shintani lifts when restricted to the space of cusp forms. As a side effect, this gives the coefficients of the classical Shintani lifts as new cycle integrals. This yields new formulas for the L-values of Hecke eigenforms. When restricted to the space of weakly holomorphic modular forms orthogonal to cusp forms, the Shintani lifts introduce a definition of weakly holomorphic Hecke eigenforms. Along the way, auxiliary lifts are constructed from the space of harmonic weak Maass forms which yield a “fractional derivative” from the space of half-integral weight harmonic weak Maass forms to half-integral weight weakly holomorphic modular forms. This fractional derivative complements the usual ξ-operator introduced by Bruinier and Funke.
Persistent Identifierhttp://hdl.handle.net/10722/197842
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorBringmann, Ken_US
dc.contributor.authorGuerzhoy, Pen_US
dc.contributor.authorKane, BRen_US
dc.date.accessioned2014-06-02T15:15:30Z-
dc.date.available2014-06-02T15:15:30Z-
dc.date.issued2014en_US
dc.identifier.citationAdvances in Mathematics, 2014, v. 255, p. 641-671en_US
dc.identifier.urihttp://hdl.handle.net/10722/197842-
dc.description.abstractIn this paper, we construct Shintani lifts from integral weight weakly holomorphic modular forms to half-integral weight weakly holomorphic modular forms. Although defined by different methods, these coincide with the classical Shintani lifts when restricted to the space of cusp forms. As a side effect, this gives the coefficients of the classical Shintani lifts as new cycle integrals. This yields new formulas for the L-values of Hecke eigenforms. When restricted to the space of weakly holomorphic modular forms orthogonal to cusp forms, the Shintani lifts introduce a definition of weakly holomorphic Hecke eigenforms. Along the way, auxiliary lifts are constructed from the space of harmonic weak Maass forms which yield a “fractional derivative” from the space of half-integral weight harmonic weak Maass forms to half-integral weight weakly holomorphic modular forms. This fractional derivative complements the usual ξ-operator introduced by Bruinier and Funke.en_US
dc.languageengen_US
dc.publisherElsevier. The Journal's web site is located at http://www.elsevier.com/locate/aimen_US
dc.relation.ispartofAdvances in Mathematicsen_US
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in Advances in Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Advances in Mathematics, 2014, v. 255, p. 641-671. DOI: 10.1016/j.aim.2014.01.015en_US
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.titleShintani lifts and fractional derivatives for harmonic weak Maass formsen_US
dc.typeArticleen_US
dc.identifier.emailKane, BR: bkane@hku.hken_US
dc.identifier.authorityKane, BR=rp01820en_US
dc.identifier.doi10.1016/j.aim.2014.01.015en_US
dc.identifier.hkuros229053en_US
dc.identifier.volume255en_US
dc.identifier.spage641en_US
dc.identifier.epage671en_US
dc.identifier.isiWOS:000334969900020-

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