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...

In mathematics, the ideal class group (or class group) of an algebraic number field K {\displaystyle K} is the quotient group J K / P K {\displaystyle...

number fields with class number 1. It is believed that there are infinitely many such number fields, but this has not been proven. The class number of...

such numbers is a special case of the class number problem, and they underlie several striking results in number theory. According to the (Baker–)Stark–Heegner...

polynomial time) is a complexity class used to classify decision problems. NP is the set of decision problems for which the problem instances, where the answer...

In statistics, the reference class problem is the problem of deciding what class to use when calculating the probability applicable to a particular case...

theory of binary quadratic forms. There remain some unsolved problems. The class number problem is particularly important. For a nonzero square free integer...

complexity class #P (pronounced "sharp P" or, sometimes "number P" or "hash P") is the set of the counting problems associated with the decision problems in the...

for this phenomenon led to the deep algebraic number theory of Heegner numbers and the class number problem. The Hardy–Littlewood conjecture F predicts...

Diophantine equations, and to solve the class number problem of finding all imaginary quadratic fields with class number 1. To simplify notation, let L {\displaystyle...

of Baker's theorem contained such bounds, solving Gauss' class number problem for class number one in the process. This work won Baker the Fields medal...

In computational complexity theory, a complexity class is a set of computational problems "of related resource-based complexity". The two most commonly...

special case of Gauss's class number problem of determining the number of imaginary quadratic fields that have a given fixed class number. Let Q denote the...

consider it to be the most important unsolved problem in pure mathematics. It is of great interest in number theory because it implies results about the...

The #P-complete problems (pronounced "sharp P complete", "number P complete", or "hash P complete") form a complexity class in computational complexity...

Gaussian period Fermat's Last Theorem Class number problem for imaginary quadratic fields Stark–Heegner theorem Heegner number Langlands program Different ideal...

problem in computer science If the solution to a problem is easy to check for correctness, must the problem be easy to solve? More unsolved problems in...

Modern Number Theory, New York, New York: Springer-Verlag, pp. 358–361, ISBN 978-0-387-97329-6 Goldfeld, Dorian (July 1985), "Gauss' Class Number Problem For...

In probability theory, the birthday problem asks for the probability that, in a set of n randomly chosen people, at least two will share the same birthday...

Boaz (Spring 2006). "Complexity of counting" (PDF). Princeton University. "counting problem". PlanetMath. "counting complexity class". PlanetMath. v t e...

{\displaystyle K} has class number 1. Given a number field, the class number is often difficult to compute. The class number problem, going back to Gauss...

from 9 distinct perfect square numbers? Class number problem: are there infinitely many real quadratic number fields with unique factorization? Fontaine–Mazur...

selected problems span a number of mathematical fields, namely algebraic geometry, arithmetic geometry, geometric topology, mathematical physics, number theory...

second problem and calling the subroutine one or more times. If both the time required to transform the first problem to the second, and the number of times...

complement problem. For example, one important problem is whether a number is a prime number. Its complement is to determine whether a number is a composite...

cover problem can be formulated as the following integer linear program (ILP). This ILP belongs to the more general class of ILPs for covering problems. The...

is the first problem that was proven to be NP-complete—this is the Cook–Levin theorem. This means that all problems in the complexity class NP, which includes...

Unsolved problem in mathematics For even numbers, divide by 2; For odd numbers, multiply by 3 and add 1. With enough repetition, do all positive integers...

Université de Montréal Gauss map in number theory Gaussian moat Gauss class number problem Gauss's multiplication formula Gaussian period Gaussian rational...

In number theory, the class number formula relates many important invariants of an algebraic number field to a special value of its Dedekind zeta function...