Links for fulltext
(May Require Subscription)
- Publisher Website: 10.1016/j.aim.2014.01.015
- Scopus: eid_2-s2.0-84893468770
- WOS: WOS:000334969900020
Supplementary
- Citations:
- Appears in Collections:
Article: Shintani lifts and fractional derivatives for harmonic weak Maass forms
Title | Shintani lifts and fractional derivatives for harmonic weak Maass forms |
---|---|
Authors | |
Keywords | Fractional-derivatives Half-integral weight harmonic weak Maass forms Hecke operators Shimura lifts Shintani lifts |
Issue Date | 2014 |
Publisher | Elsevier. 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? |
Abstract | In 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 Identifier | http://hdl.handle.net/10722/197842 |
ISI Accession Number ID |
DC Field | Value | Language |
---|---|---|
dc.contributor.author | Bringmann, K | en_US |
dc.contributor.author | Guerzhoy, P | en_US |
dc.contributor.author | Kane, BR | en_US |
dc.date.accessioned | 2014-06-02T15:15:30Z | - |
dc.date.available | 2014-06-02T15:15:30Z | - |
dc.date.issued | 2014 | en_US |
dc.identifier.citation | Advances in Mathematics, 2014, v. 255, p. 641-671 | en_US |
dc.identifier.uri | http://hdl.handle.net/10722/197842 | - |
dc.description.abstract | In 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.language | eng | en_US |
dc.publisher | Elsevier. The Journal's web site is located at http://www.elsevier.com/locate/aim | en_US |
dc.relation.ispartof | Advances in Mathematics | en_US |
dc.rights | NOTICE: 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.2014.01.015 | en_US |
dc.rights | This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | - |
dc.subject | Fractional-derivatives | - |
dc.subject | Half-integral weight harmonic weak Maass forms | - |
dc.subject | Hecke operators | - |
dc.subject | Shimura lifts | - |
dc.subject | Shintani lifts | - |
dc.title | Shintani lifts and fractional derivatives for harmonic weak Maass forms | 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 | 10.1016/j.aim.2014.01.015 | en_US |
dc.identifier.scopus | eid_2-s2.0-84893468770 | - |
dc.identifier.hkuros | 229053 | en_US |
dc.identifier.volume | 255 | en_US |
dc.identifier.spage | 641 | en_US |
dc.identifier.epage | 671 | en_US |
dc.identifier.isi | WOS:000334969900020 | - |