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- Stark–Heegner_theorem abstract "In number theory, a branch of mathematics, the Stark–Heegner theorem states precisely which quadratic imaginary number fields admit unique factorisation in their ring of integers. It solves a 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 set of rational numbers, and let d be a square-free integer (i.e., a product of distinct primes) other than 1. Then Q(√d) is a finite extension of Q, called a quadratic extension. The class number of Q(√d) is the number of equivalence classes of ideals of the ring of integers of Q(√d), where two ideals I and J are equivalent if and only if there exist principal ideals (a) and (b) such that (a)I = (b)J. Thus, the ring of integers of Q(√d) is a principal ideal domain (and hence a unique factorization domain) if and only if the class number of Q(√d) is equal to 1. The Stark–Heegner theorem can then be stated as follows:If d < 0, then the class number of Q(√d) is equal to 1 if and only if These are known as the Heegner numbers.This list is also written, replacing −1 with −4 and −2 with −8 (which does not change the field), as:where D is interpreted as the discriminant (either of the number field or of an elliptic curve with complex multiplication).".
- Stark–Heegner_theorem wikiPageID "391251".
- Stark–Heegner_theorem wikiPageRevisionID "579599287".
- Stark–Heegner_theorem subject Category:Theorems_in_algebraic_number_theory.
- Stark–Heegner_theorem comment "In number theory, a branch of mathematics, the Stark–Heegner theorem states precisely which quadratic imaginary number fields admit unique factorisation in their ring of integers. It solves a 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 set of rational numbers, and let d be a square-free integer (i.e., a product of distinct primes) other than 1.".
- Stark–Heegner_theorem label "Stark–Heegner theorem".
- Stark–Heegner_theorem label "Stelling van Stark-Heegner".
- Stark–Heegner_theorem label "Théorème de Stark-Heegner".
- Stark–Heegner_theorem sameAs Stark%E2%80%93Heegner_theorem.
- Stark–Heegner_theorem sameAs Théorème_de_Stark-Heegner.
- Stark–Heegner_theorem sameAs Stelling_van_Stark-Heegner.
- Stark–Heegner_theorem sameAs Q2793600.
- Stark–Heegner_theorem sameAs Q2793600.
- Stark–Heegner_theorem wasDerivedFrom Stark–Heegner_theorem?oldid=579599287.