New modular relations for cubics class invariants


In this paper, we establish several new P–Q mixed modular equations involving theta–functions which are similar to those recorded by Ramanujan in his notebooks. As an application, we establish several new explicit evaluations of cubic class invariants and cubic singular moduli.

DOI Code: 10.1285/i15900932v34n2p75

Keywords: Modular equations; Theta–functions; cubic class invariant; cubic singular moduli

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