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Article: Ramanujan-like formulas for Fourier coefficients of all meromorphic cusp forms
Title | Ramanujan-like formulas for Fourier coefficients of all meromorphic cusp forms |
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Authors | |
Keywords | Meromorphic modular forms Quasi-meromorphic modular forms Fourier coefficients Ramanujan-type formulas Polar harmonic Maass forms |
Issue Date | 2020 |
Publisher | Academic Press. The Journal's web site is located at http://www.elsevier.com/locate/aim |
Citation | Advances in Mathematics, 2020, v. 373, p. article no. 107308 How to Cite? |
Abstract | In this paper, we investigate Fourier expansions of meromorphic modular forms. Over the years, a number of special cases of meromorphic modular forms were shown to have Fourier expansions closely resembling the expansion of the reciprocal of the weight 6 Eisenstein series which was computed by Hardy and Ramanujan. By investigating meromorphic modular forms within a larger space of so-called polar harmonic Maass forms, we prove in this paper that all negative-weight meromorphic modular forms (and furthermore all quasi-meromorphic modular forms) have Fourier expansions of this type, granted that they are bounded towards infinity. |
Persistent Identifier | http://hdl.handle.net/10722/284072 |
ISSN | 2023 Impact Factor: 1.5 2023 SCImago Journal Rankings: 2.022 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Bringmann, K | - |
dc.contributor.author | Kane, B | - |
dc.date.accessioned | 2020-07-20T05:55:52Z | - |
dc.date.available | 2020-07-20T05:55:52Z | - |
dc.date.issued | 2020 | - |
dc.identifier.citation | Advances in Mathematics, 2020, v. 373, p. article no. 107308 | - |
dc.identifier.issn | 0001-8708 | - |
dc.identifier.uri | http://hdl.handle.net/10722/284072 | - |
dc.description.abstract | In this paper, we investigate Fourier expansions of meromorphic modular forms. Over the years, a number of special cases of meromorphic modular forms were shown to have Fourier expansions closely resembling the expansion of the reciprocal of the weight 6 Eisenstein series which was computed by Hardy and Ramanujan. By investigating meromorphic modular forms within a larger space of so-called polar harmonic Maass forms, we prove in this paper that all negative-weight meromorphic modular forms (and furthermore all quasi-meromorphic modular forms) have Fourier expansions of this type, granted that they are bounded towards infinity. | - |
dc.language | eng | - |
dc.publisher | Academic Press. The Journal's web site is located at http://www.elsevier.com/locate/aim | - |
dc.relation.ispartof | Advances in Mathematics | - |
dc.subject | Meromorphic modular forms | - |
dc.subject | Quasi-meromorphic modular forms | - |
dc.subject | Fourier coefficients | - |
dc.subject | Ramanujan-type formulas | - |
dc.subject | Polar harmonic Maass forms | - |
dc.title | Ramanujan-like formulas for Fourier coefficients of all meromorphic cusp forms | - |
dc.type | Article | - |
dc.identifier.email | Kane, B: bkane@hku.hk | - |
dc.identifier.authority | Kane, B=rp01820 | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1016/j.aim.2020.107308 | - |
dc.identifier.scopus | eid_2-s2.0-85088783806 | - |
dc.identifier.hkuros | 310825 | - |
dc.identifier.volume | 373 | - |
dc.identifier.spage | article no. 107308 | - |
dc.identifier.epage | article no. 107308 | - |
dc.identifier.isi | WOS:000566696200005 | - |
dc.publisher.place | United Kingdom | - |
dc.identifier.issnl | 0001-8708 | - |