Chandrashekar Adiga

Learn More
In this paper we give two integral representations for the Ramanujan's cubic continued fraction V (q) and also derive a modular equation relating V (q) and V (q 3). We also establish some modular equations and a transformation formula for Ra-manujan's theta-function. As an application of these, we compute several new explicit evaluations of theta-functions(More)
Recently, the authors have established a large class of modular relations involving the Rogers-Ramanujan type functions J(q) and K(q) of order ten. In this paper, we establish further modular relations connecting these two functions with Rogers-Ramanujan functions, Göllnitz-Gordon functions and cubic functions, which are analogues to the Ramanujan's forty(More)
Let λ = (λ1, · · · , λm) be a partition of k. Let r λ (n) denote the number of solutions in integers of λ1x 2 1 + · · · + λmx 2 m = n, and let t λ (n) denote the number of solutions in non negative integers of λ1x1(x1 + 1)/2 + · · · + λmxm(xm + 1)/2 = n. We prove that if 1 ≤ k ≤ 7, then there is a constant c λ , depending only on λ, such that r λ (8n + k) =(More)