So Berndt doesn't consider the Brocard-Ramanujan problem to be a "remaining conjecture" of Ramanujan, I guess? Or maybe he was considering only "formulas" because you were limiting yourself to formulas?
Here is a mistake which was even featured in the Ramanujan movie: in his letters to Hardy, Ramanujan claimed to have found an exact formula for the prime counting function $\pi (n)$, but (in Hardy's words) Ramanujan’s theory of primes was vitiated by his ignorance of the theory of functions of a complex variable.
Riemann Hypothesis and Ramanujan’s Sum Explanation RH: All non-trivial zeros of the Riemannian zeta-function lie on the critical line. ERH: All zeros of L-functions to complex Dirichlet characters of finite cyclic groups within the critical strip lie on the critical line. Related Article: The History and Importance of the Riemann Hypothesis The goal of this article is to provide the ...
0 Ramanujan's famous pi formula states that \begin {equation} \frac {1} {\pi}=\frac {2\sqrt {2}} {99^2}\sum_ {k=0}^ {\infty}\frac { (4k)!} {k!^4}\frac {26390k+1103} {396^ {4k}} \end {equation} How can one prove this? If the proof is too long for this site, you can reference any article containing the proof.
Why was Ramanujan interested in the his tau function before the advent of modular forms? The machinery of modular forms used by Mordel to solve the multiplicative property seems out of context unti...
How do we explain why the same quartic in $k$ has appeared four times now: when using the elliptic lambda $\lambda (\tau)$, Rogers-Ramanujan continued fraction $R (q)$, Jacobi theta $\vartheta_4 (0,q)$, and the Ramanujan g-function $g (\tau)$?
modular forms - Solving the Bring quintic using the Ramanujan $g$- and ...