"It's almost an integer"

Starting many years ago with somebody in a pub who told me about the n=163 case, I computed a bunch of them here. It being the early days of the internet, I made a web page, because what else do you do?

Ten years later, at a used book sale, I came across the Collected Papers of Ramanujan, and one particular paper caught my eye: Modular equations and approximations to π. You can see he is hot on the trail!

Below is my program of learning. I want to understand all this about the j-invariant, what is a class number, and why the j-invariant is an integer at these special points.

“Introduction to Modular Forms,” by Keith Conrad.
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"A Short Course on Modular Forms" by Prof. M. Ram Murty
1 2 3 4 5 6 7 8 9 10

"j-function", a Wolfram notebook
pdf

"Class number statistics for imaginary quadratic fields" by Pär Kurlberg
youtube

"Gauss' class number problem for imaginary quadratic fields" by Dorian Goldfeld
pdf

"Modular curves and the class number one problem" by Jeremy Booher
pdf