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math.NT2020
Applications of a new P-Q modular equation of degree two
D. J. Prabhakaran, K. Ranjith kumar
At scattered places in his first notebook, Ramanujan recorded the values for 107 class invariants or irreducible monic polynomials satisfied by them. On pages 294-299 in his second…
math.NT2020
The explicit evaluations of Ramanujan's remarkable product of theta-functions a_{m, n}
D. J. Prabhakaran, K. Ranjith kumar
On pages 338 and 339 in his first notebook, Ramanujan defined the remarkable product of theta-functions . Also he recorded eighteen explicit values depending on two param…
math.NT2020
The Explicit Evaluations Formula for Ramanujan's Singular Moduli and Ramanujan- Selberg Continued Fraction
D. J. Prabhakaran, K. Ranjith kumar
At scattered places of his notebooks, Ramanujan recorded over 30 values of singular moduli . All those results were proved by Berndt et. al by employing Weber-Ramanujan's clas…