Class Number Problem

(Algebraic Number Theory)

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Algebraic Number Theory
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What is 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 (for negative integers d) 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 . 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.

Technology Types

algebraic number theoryconditiondifficultymathematical problemproblemunsolved problems in mathematic

Synonyms

Class number 1 problemClass number conjectureClass number one problemClass number problem for imaginary quadratic fields

Translations

Klassegetalprobleem (nl)Problème du nombre de classes pour les corps quadratiques imaginaires (fr)類数問題 (ja)

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