As I was flipping through the scanned version of Ramanujan's "Lost Notebook" in our library, I came across a result which caught my attention. And as any excited teenager would do, I immediately photographed that page and put it up here.

The result in the photo is as follows.

If $S(N)$ be the number of ways in which $N$ can be expressed as the sum of 2 squares, then the max. order of $S(N)$ $$= \sqrt{\text{max order of }\\ d(N^2 +aN+b)} \cdot e^{O(\log N)^{1/2 + \epsilon}}$$

Has anyone come across any such result before? Is this result true?