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- Chebotarev's_density_theorem abstract "Chebotarev's density theorem in algebraic number theory describes statistically the splitting of primes in a given Galois extension K of the field Q of rational numbers. Generally speaking, a prime integer will factor into several ideal primes in the ring of algebraic integers of K. There are only finitely many patterns of splitting that may occur. Although the full description of the splitting of every prime p in a general Galois extension is a major unsolved problem, the Chebotarev density theorem says that the frequency of the occurrence of a given pattern, for all primes p less than a large integer N, tends to a certain limit as N goes to infinity. It was proved by Nikolai Chebotaryov in his thesis in 1922, published in (Tschebotareff 1926).A special case that is easier to state says that if K is an algebraic number field which is a Galois extension of Q of degree n, then the prime numbers that completely split in K have density 1/namong all primes. More generally, splitting behavior can be specified by assigning to (almost) every prime number an invariant, its Frobenius element, which strictly is a representative of a well-defined conjugacy class in the Galois group Gal(K/Q).Then the theorem says that the asymptotic distribution of these invariants is uniform over the group, so that a conjugacy class with k elements occurs with frequency asymptotic to k/n.".
- Chebotarev's_density_theorem wikiPageExternalLink chebotarev.pdf.
- Chebotarev's_density_theorem wikiPageID "535349".
- Chebotarev's_density_theorem wikiPageRevisionID "573536463".
- Chebotarev's_density_theorem hasPhotoCollection Chebotarev's_density_theorem.
- Chebotarev's_density_theorem subject Category:Analytic_number_theory.
- Chebotarev's_density_theorem subject Category:Theorems_in_algebraic_number_theory.
- Chebotarev's_density_theorem type Abstraction100002137.
- Chebotarev's_density_theorem type Communication100033020.
- Chebotarev's_density_theorem type Message106598915.
- Chebotarev's_density_theorem type Proposition106750804.
- Chebotarev's_density_theorem type Statement106722453.
- Chebotarev's_density_theorem type Theorem106752293.
- Chebotarev's_density_theorem type TheoremsInAlgebraicNumberTheory.
- Chebotarev's_density_theorem comment "Chebotarev's density theorem in algebraic number theory describes statistically the splitting of primes in a given Galois extension K of the field Q of rational numbers. Generally speaking, a prime integer will factor into several ideal primes in the ring of algebraic integers of K. There are only finitely many patterns of splitting that may occur.".
- Chebotarev's_density_theorem label "Chebotarev's density theorem".
- Chebotarev's_density_theorem label "Théorème de densité de Tchebotariov".
- Chebotarev's_density_theorem label "Tschebotarjowscher Dichtigkeitssatz".
- Chebotarev's_density_theorem sameAs Tschebotarjowscher_Dichtigkeitssatz.
- Chebotarev's_density_theorem sameAs Théorème_de_densité_de_Tchebotariov.
- Chebotarev's_density_theorem sameAs m.02mmyb.
- Chebotarev's_density_theorem sameAs Q1425529.
- Chebotarev's_density_theorem sameAs Q1425529.
- Chebotarev's_density_theorem sameAs Chebotarev's_density_theorem.
- Chebotarev's_density_theorem wasDerivedFrom Chebotarev's_density_theorem?oldid=573536463.
- Chebotarev's_density_theorem isPrimaryTopicOf Chebotarev's_density_theorem.