Ramanujan's Eisenstein series and powers of Dedekind's eta-function

• Autores: Heng Huat Chan, Shaun Cooper, Pee Choon Toh
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 75, Nº 1, 2007, págs. 225-242
• Idioma: inglés
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• Resumen

  • In this article, we use the theory of elliptic functions to construct theta function identities which are equivalent to Macdonald's identities for A2, B2 and G2. Using these identities, we express, for d = 8, 10 or 14, certain theta functions in the form d()F(P, Q, R), where () is Dedekind's eta-function, and F(P, Q, R) is a polynomial in Ramanujan's Eisenstein series P, Q and R. We also derive identities in the case when d = 26. These lead to a new expression for 26(). This work generalizes the results for d = 1 and d = 3 which were given by Ramanujan on page 369 of ¿The Lost Notebook¿