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- Chebotarevs_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.".
- Chebotarevs_density_theorem wikiPageExternalLink chebotarev.pdf.
- Chebotarevs_density_theorem wikiPageID "535349".
- Chebotarevs_density_theorem wikiPageLength "10949".
- Chebotarevs_density_theorem wikiPageOutDegree "39".
- Chebotarevs_density_theorem wikiPageRevisionID "646491606".
- Chebotarevs_density_theorem wikiPageWikiLink Abelian_extension.
- Chebotarevs_density_theorem wikiPageWikiLink Algebraic_conjugate.
- Chebotarevs_density_theorem wikiPageWikiLink Algebraic_integer.
- Chebotarevs_density_theorem wikiPageWikiLink Algebraic_number_field.
- Chebotarevs_density_theorem wikiPageWikiLink Algebraic_number_theory.
- Chebotarevs_density_theorem wikiPageWikiLink Carl_Friedrich_Gauss.
- Chebotarevs_density_theorem wikiPageWikiLink Category:Analytic_number_theory.
- Chebotarevs_density_theorem wikiPageWikiLink Category:Theorems_in_algebraic_number_theory.
- Chebotarevs_density_theorem wikiPageWikiLink Characteristic_(algebra).
- Chebotarevs_density_theorem wikiPageWikiLink Chebotarev_density_theorem.
- Chebotarevs_density_theorem wikiPageWikiLink Chebotarevs_density_theorem.
- Chebotarevs_density_theorem wikiPageWikiLink Conjugacy_class.
- Chebotarevs_density_theorem wikiPageWikiLink Conjugate_(algebra).
- Chebotarevs_density_theorem wikiPageWikiLink Coprime.
- Chebotarevs_density_theorem wikiPageWikiLink Coprime_integers.
- Chebotarevs_density_theorem wikiPageWikiLink Cycle_representation.
- Chebotarevs_density_theorem wikiPageWikiLink Cyclotomic_field.
- Chebotarevs_density_theorem wikiPageWikiLink Dirichlets_theorem_on_arithmetic_progressions.
- Chebotarevs_density_theorem wikiPageWikiLink Euler_totient_function.
- Chebotarevs_density_theorem wikiPageWikiLink Eulers_totient_function.
- Chebotarevs_density_theorem wikiPageWikiLink Ferdinand_Georg_Frobenius.
- Chebotarevs_density_theorem wikiPageWikiLink Frobenius_element.
- Chebotarevs_density_theorem wikiPageWikiLink Frobenius_endomorphism.
- Chebotarevs_density_theorem wikiPageWikiLink Galois_extension.
- Chebotarevs_density_theorem wikiPageWikiLink Galois_group.
- Chebotarevs_density_theorem wikiPageWikiLink Gaussian_integer.
- Chebotarevs_density_theorem wikiPageWikiLink Georg_Frobenius.
- Chebotarevs_density_theorem wikiPageWikiLink Ideal_number.
- Chebotarevs_density_theorem wikiPageWikiLink Klein_four-group.
- Chebotarevs_density_theorem wikiPageWikiLink Natural_density.
- Chebotarevs_density_theorem wikiPageWikiLink Nikolai_Chebotaryov.
- Chebotarevs_density_theorem wikiPageWikiLink Nikolai_Grigoryevich_Chebotaryov.
- Chebotarevs_density_theorem wikiPageWikiLink Partition_(number_theory).
- Chebotarevs_density_theorem wikiPageWikiLink Partition_of_an_integer.
- Chebotarevs_density_theorem wikiPageWikiLink Permutation.
- Chebotarevs_density_theorem wikiPageWikiLink Prime_field.
- Chebotarevs_density_theorem wikiPageWikiLink Prime_number.
- Chebotarevs_density_theorem wikiPageWikiLink Rational_number.
- Chebotarevs_density_theorem wikiPageWikiLink Rational_number_field.
- Chebotarevs_density_theorem wikiPageWikiLink Splitting_field.
- Chebotarevs_density_theorem wikiPageWikiLink Symmetric_group.
- Chebotarevs_density_theorem wikiPageWikiLinkText "Chebotarev's density theorem".
- Chebotarevs_density_theorem hasPhotoCollection Chebotarevs_density_theorem.
- Chebotarevs_density_theorem wikiPageUsesTemplate Template:Citation.
- Chebotarevs_density_theorem wikiPageUsesTemplate Template:Harv.
- Chebotarevs_density_theorem wikiPageUsesTemplate Template:Harvtxt.
- Chebotarevs_density_theorem wikiPageUsesTemplate Template:Neukirch_ANT.
- Chebotarevs_density_theorem subject Category:Analytic_number_theory.
- Chebotarevs_density_theorem subject Category:Theorems_in_algebraic_number_theory.
- Chebotarevs_density_theorem type Thing.
- Chebotarevs_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.".
- Chebotarevs_density_theorem label "Chebotarev's density theorem".
- Chebotarevs_density_theorem sameAs Tschebotarjowscher_Dichtigkeitssatz.
- Chebotarevs_density_theorem sameAs Tšebotarevin_tiheyslause.
- Chebotarevs_density_theorem sameAs Théorème_de_densité_de_Tchebotariov.
- Chebotarevs_density_theorem sameAs xd7x9exd7xa9xd7xa4xd7x98_xd7x94xd7xa6xd7xa4xd7x99xd7xa4xd7x95xd7xaa_xd7xa9xd7x9c_xd7xa6xd7x91xd7x95xd7x98xd7xa8xd7x91.
- Chebotarevs_density_theorem sameAs m.02mmyb.
- Chebotarevs_density_theorem sameAs Q1425529.
- Chebotarevs_density_theorem sameAs Q1425529.
- Chebotarevs_density_theorem wasDerivedFrom Chebotarevs_density_theoremoldid=646491606.
- Chebotarevs_density_theorem isPrimaryTopicOf Chebotarevs_density_theorem.