What is Class number problem?

In mathematics, the Gauss class number problem , as usually understood, is to provide for each n ≥ 1 a complete list of imaginary quadratic fields Q {\displaystyle \mathbb {Q} } having class number n. It is named after Carl Friedrich Gauss. It can also be stated in terms of discriminants. There are related questions for real quadratic fields and for the behavior as d → − ∞ {\displaystyle d\to -\infty }.

The difficulty is in effective computation of bounds: for a given discriminant, it is easy to compute the class number, and there are several ineffective lower bounds on class number , but effective bounds are harder.