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Article: Ramanujan-like formulas for Fourier coefficients of all meromorphic cusp forms

TitleRamanujan-like formulas for Fourier coefficients of all meromorphic cusp forms
Authors
KeywordsMeromorphic modular forms
Quasi-meromorphic modular forms
Fourier coefficients
Ramanujan-type formulas
Polar harmonic Maass forms
Issue Date2020
PublisherAcademic 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?
AbstractIn 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 Identifierhttp://hdl.handle.net/10722/284072
ISSN
2023 Impact Factor: 1.5
2023 SCImago Journal Rankings: 2.022
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorBringmann, K-
dc.contributor.authorKane, B-
dc.date.accessioned2020-07-20T05:55:52Z-
dc.date.available2020-07-20T05:55:52Z-
dc.date.issued2020-
dc.identifier.citationAdvances in Mathematics, 2020, v. 373, p. article no. 107308-
dc.identifier.issn0001-8708-
dc.identifier.urihttp://hdl.handle.net/10722/284072-
dc.description.abstractIn 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.languageeng-
dc.publisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/aim-
dc.relation.ispartofAdvances in Mathematics-
dc.subjectMeromorphic modular forms-
dc.subjectQuasi-meromorphic modular forms-
dc.subjectFourier coefficients-
dc.subjectRamanujan-type formulas-
dc.subjectPolar harmonic Maass forms-
dc.titleRamanujan-like formulas for Fourier coefficients of all meromorphic cusp forms-
dc.typeArticle-
dc.identifier.emailKane, B: bkane@hku.hk-
dc.identifier.authorityKane, B=rp01820-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1016/j.aim.2020.107308-
dc.identifier.scopuseid_2-s2.0-85088783806-
dc.identifier.hkuros310825-
dc.identifier.volume373-
dc.identifier.spagearticle no. 107308-
dc.identifier.epagearticle no. 107308-
dc.identifier.isiWOS:000566696200005-
dc.publisher.placeUnited Kingdom-
dc.identifier.issnl0001-8708-

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