Editing Class number problem (section)

{{Short description|Listing all imaginary quadratic fields with a given class number}}
In [[mathematics]], the '''Gauss class number problem''' ('''for imaginary quadratic fields'''), as usually understood, is to provide for each ''n''&nbsp;≥&nbsp;1 a complete list of [[imaginary quadratic field]]s <math>\mathbb{Q}(\sqrt{d})</math> (for negative integers ''d'') having [[class number (number theory)|class number]] ''n''. It is named after [[Carl Friedrich Gauss]]. It can also be stated in terms of [[Discriminant of an algebraic number field|discriminants]]. There are related questions for real quadratic fields and for the behavior as <math>d \to -\infty</math>.

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 (meaning that they involve a constant that is not computed), but effective bounds (and explicit proofs of completeness of lists) are harder.