Pushpa, K. and Vasuki, K. R. (2022) On Ramanujan's Eisenstein series of level 5 and 7. Journal of the Ramanujan Mathematical Society, 37 (3). pp. 257-272. ISSN 2320-3110
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Ramanujan recorded eight Eisenstein series identities of level 5 and 7 (Four in each level). These identities have been proved for the first time by S. Raghavan and S. S. Rangachari using the theory of modular forms. B. C. Berndt et al have constructed the proofs of these identities in the spirit of Ramanujan's work. In fact, they acknowledged the usage of Mathematica often times for algebraic manipulations in their proofs. S. Cooper proved quintic level identities by using the parametrization k = r(q)r(2)(q(2)), where r(q) is the famous Rogers-Ramanujan continued fraction. Z.-G. Liu found proofs of septic level identities using the complex variable theory of elliptic functions. Our objective of this article is to give a simple proofs of these identities by using only P-Q theta function identities recorded by Ramanujan.
| Item Type: | Article |
|---|---|
| Subjects: | E Mathematical Science > Mathematics |
| Divisions: | Department of > Mathematics |
| Depositing User: | C Swapna Library Assistant |
| Date Deposited: | 14 Jul 2023 09:32 |
| Last Modified: | 14 Jul 2023 09:32 |
| URI: | http://eprints.uni-mysore.ac.in/id/eprint/17627 |
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