File Download

There are no files associated with this item.

  Links for fulltext
     (May Require Subscription)
Supplementary

Article: Ramanujan and coefficients of meromorphic modular forms

TitleRamanujan and coefficients of meromorphic modular forms
Authors
Issue Date2016
Citation
Journal de Mathématiques Pures et Appliquées, 2016 How to Cite?
AbstractThe 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 Identifierhttp://hdl.handle.net/10722/223854

 

DC FieldValueLanguage
dc.contributor.authorBringmann, K-
dc.contributor.authorKane, BR-
dc.date.accessioned2016-03-18T02:29:59Z-
dc.date.available2016-03-18T02:29:59Z-
dc.date.issued2016-
dc.identifier.citationJournal de Mathématiques Pures et Appliquées, 2016-
dc.identifier.urihttp://hdl.handle.net/10722/223854-
dc.description.abstractThe 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.languageeng-
dc.relation.ispartofJournal de Mathématiques Pures et Appliquées-
dc.rights© <2016>. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/-
dc.titleRamanujan and coefficients of meromorphic modular forms-
dc.typeArticle-
dc.identifier.emailKane, BR: bkane@hku.hk-
dc.identifier.authorityKane, BR=rp01820-
dc.identifier.doi10.1016/j.matpur.2016.04.009-
dc.identifier.hkuros257241-

Export via OAI-PMH Interface in XML Formats


OR


Export to Other Non-XML Formats