Feb 7, 2014
Eisenstein series identities based on partial fraction decomposition
RAMANUJAN JOURNAL
- ,
- ,
- Volume
- 38
- Number
- 3
- First page
- 455
- Last page
- 463
- Language
- English
- Publishing type
- DOI
- 10.1007/s11139-014-9639-7
- Publisher
- SPRINGER
From the theory of modular forms, there are exactly $[(k-2)/6]$ linear
relations among the Eisenstein series $E_k$ and its products $E_{2i}E_{k-2i}\
(2\le i \le [k/4])$. We present explicit formulas among these modular forms
based on the partial fraction decomposition, and use them to determining a
basis of the space of modular forms of weight $k$ on ${\rm SL}_2({\mathbb Z})$.
relations among the Eisenstein series $E_k$ and its products $E_{2i}E_{k-2i}\
(2\le i \le [k/4])$. We present explicit formulas among these modular forms
based on the partial fraction decomposition, and use them to determining a
basis of the space of modular forms of weight $k$ on ${\rm SL}_2({\mathbb Z})$.
- Link information
-
- DOI
- https://doi.org/10.1007/s11139-014-9639-7
- J-GLOBAL
- https://jglobal.jst.go.jp/en/detail?JGLOBAL_ID=201702215252961870
- arXiv
- http://arxiv.org/abs/arXiv:1402.1585
- Web of Science
- https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=JSTA_CEL&SrcApp=J_Gate_JST&DestLinkType=FullRecord&KeyUT=WOS:000364969700001&DestApp=WOS_CPL
- URL
- http://arxiv.org/abs/1402.1585v1
- URL
- http://arxiv.org/pdf/1402.1585v1 Open access
- ID information
-
- DOI : 10.1007/s11139-014-9639-7
- ISSN : 1382-4090
- eISSN : 1572-9303
- J-Global ID : 201702215252961870
- arXiv ID : arXiv:1402.1585
- Web of Science ID : WOS:000364969700001