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On a Ramanujan's Eisenstein series identity of level fifteen.
- Source :
-
Proceedings of the Indian Academy of Sciences: Mathematical Sciences . Sep2019, Vol. 129 Issue 4, pN.PAG-N.PAG. 1p. - Publication Year :
- 2019
-
Abstract
- On pages 255–256 of his second notebook, Ramanujan recorded an Eisenstein series identity of level 15 without offering a proof. Previously, Berndt (Ramanujan's Notebooks: Part III (1991) (New York: Springer)) proved this identity using the theory of modular forms. In this paper, we give an elementary proof of this identity. In the process, we also give an elementary proof of three Ramanujan's P - Q identities of level 15. Further, using the P - Q identities we prove four Ramanujan type Eisenstein series of level 15 due to Cooper and Ye (Trans. Am. Math. Soc.368 (2016) 7883–7910), where they have proved using the theory of modular forms. [ABSTRACT FROM AUTHOR]
- Subjects :
- *MODULAR forms
*EISENSTEIN series
*MATHEMATICS
*EVIDENCE
Subjects
Details
- Language :
- English
- ISSN :
- 02534142
- Volume :
- 129
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Proceedings of the Indian Academy of Sciences: Mathematical Sciences
- Publication Type :
- Academic Journal
- Accession number :
- 137624723
- Full Text :
- https://doi.org/10.1007/s12044-019-0498-4