arXiv subjects
Publications and source records attributed to M. S. Mahadeva Naika.
In his second notebook, Ramanujan recorded total of 23 P-Q modular equations involving theta-functions $f(-q)$, $φ(q)$ and $ψ(q)$. In this paper, modular equations analogous to those recorded by Ramanujan are obtained involving $f(-q)$. As a consequence, values of certain quotients of theta-function are evaluated.
Let $a_3(n)$ and $a_9(n)$ are 3 and 9-regular cubic partitions of $n$. In this paper, we find the infinite family of congruences modulo powers of 3 for $a_3(n)$ and $a_9(n)$ such as \[a_3\left (3^{2α}n+\frac{3^{2α}-1}{4}\right )\equiv 0 \pmod{3^α}\] and \[a_9\left (3^{α+1}n+3^{α+1}-1\right )\equiv 0 \pmod{3^{α+1}}.\]
We study Ramanujan's cubic continued fraction and explicit evaluations of theta-functions