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Article: Ramanujan and coefficients of meromorphic modular forms
Title | Ramanujan and coefficients of meromorphic modular forms |
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Authors | |
Keywords | Fourier coefficients Meromorphic modular forms Poincaré series Quasi-modular forms Ramanujan |
Issue Date | 2017 |
Publisher | Elsevier France, Editions Scientifiques et Medicales. The Journal's web site is located at http://www.elsevier.com/locate/matpur |
Citation | Journal de Mathematiques Pures et Appliquees, 2017, v. 107 n. 1, p. 100-122 How to Cite? |
Abstract | The study of Fourier coefficients of meromorphic modular forms dates back to Ramanujan, who, together with Hardy, studied the reciprocal of the weight 6 Eisenstein series. Ramanujan conjectured a number of further identities for other meromorphic modular forms and quasi-modular forms which were subsequently established by Berndt, Bialek, and Yee. In this paper, we place these identities into the context of a larger family by making use of Poincaré series introduced by Petersson and a new family of Poincaré series which we construct here and which are of independent interest. In addition we establish a number of new explicit identities. In particular, we give the first examples of Fourier expansions for meromorphic modular form with third-order poles and quasi-meromorphic modular forms with second-order poles. |
Persistent Identifier | http://hdl.handle.net/10722/223854 |
ISSN | 2023 Impact Factor: 2.1 2023 SCImago Journal Rankings: 2.487 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Bringmann, K | - |
dc.contributor.author | Kane, BR | - |
dc.date.accessioned | 2016-03-18T02:29:59Z | - |
dc.date.available | 2016-03-18T02:29:59Z | - |
dc.date.issued | 2017 | - |
dc.identifier.citation | Journal de Mathematiques Pures et Appliquees, 2017, v. 107 n. 1, p. 100-122 | - |
dc.identifier.issn | 0021-7824 | - |
dc.identifier.uri | http://hdl.handle.net/10722/223854 | - |
dc.description.abstract | The study of Fourier coefficients of meromorphic modular forms dates back to Ramanujan, who, together with Hardy, studied the reciprocal of the weight 6 Eisenstein series. Ramanujan conjectured a number of further identities for other meromorphic modular forms and quasi-modular forms which were subsequently established by Berndt, Bialek, and Yee. In this paper, we place these identities into the context of a larger family by making use of Poincaré series introduced by Petersson and a new family of Poincaré series which we construct here and which are of independent interest. In addition we establish a number of new explicit identities. In particular, we give the first examples of Fourier expansions for meromorphic modular form with third-order poles and quasi-meromorphic modular forms with second-order poles. | - |
dc.language | eng | - |
dc.publisher | Elsevier France, Editions Scientifiques et Medicales. The Journal's web site is located at http://www.elsevier.com/locate/matpur | - |
dc.relation.ispartof | Journal de Mathematiques Pures et Appliquees | - |
dc.rights | This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | - |
dc.subject | Fourier coefficients | - |
dc.subject | Meromorphic modular forms | - |
dc.subject | Poincaré series | - |
dc.subject | Quasi-modular forms | - |
dc.subject | Ramanujan | - |
dc.title | Ramanujan and coefficients of meromorphic modular forms | - |
dc.type | Article | - |
dc.identifier.email | Kane, BR: bkane@hku.hk | - |
dc.identifier.authority | Kane, BR=rp01820 | - |
dc.description.nature | postprint | - |
dc.identifier.doi | 10.1016/j.matpur.2016.04.009 | - |
dc.identifier.scopus | eid_2-s2.0-85006265928 | - |
dc.identifier.hkuros | 257241 | - |
dc.identifier.volume | 107 | - |
dc.identifier.issue | 1 | - |
dc.identifier.spage | 100 | - |
dc.identifier.epage | 122 | - |
dc.identifier.isi | WOS:000392039500004 | - |
dc.publisher.place | France | - |
dc.identifier.issnl | 0021-7824 | - |