Class Number Problem

Class Number Problem

In mathematics, the Gauss class number problem (for imaginary quadratic fields), as usually understood, is to provide for each n ≥ 1 a complete list of imaginary quadratic fields with class number n. It is named after the great mathematician Carl Friedrich Gauss. It can also be stated in terms of discriminants. There are related questions for real quadratic fields and the behavior as

.

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.

Read more about Class Number Problem:  Gauss's Original Conjectures, Status, Lists of Discriminants of Class Number 1, Modern Developments, Real Quadratic Fields

Famous quotes containing the words class, number and/or problem:

    “There is still the feeling that women’s writing is a lesser class of writing, that ... what goes on in the nursery or the bedroom is not as important as what goes on in the battlefield, ... that what women know about is a less category of knowledge.”
    —Erica Jong (b. 1942)

    “Today, almost forty years later, I grow dizzy when I recall that the number of manufactured tanks seems to have been more important to me than the vanished victims of racism.”
    —Albert Speer (1905–1981)

    “The perfect detective story cannot be written. The type of mind which can evolve the perfect problem is not the type of mind that can produce the artistic job of writing.”
    —Raymond Chandler (1888–1959)