Unsolved problems in number theory | Mathematical problems | Algebraic number theory

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. (Wikipedia).

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Related pages

Carl Friedrich Gauss | Disquisitiones Arithmeticae | Fundamental unit (number theory) | Effective results in number theory | Discriminant of an algebraic number field | Elliptic curve | Hans Heilbronn | L-function | List of number fields with class number one | Heegner number | Mathematics | Modular form | Stark–Heegner theorem | Modular equation | Baker's theorem | Alan Baker (mathematician) | Algebraic number