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- Hilberts_twelfth_problem abstract "Kronecker's Jugendtraum or Hilbert's twelfth problem, of the 23 mathematical Hilbert problems, is the extension of the Kronecker–Weber theorem on abelian extensions of the rational numbers, to any base number field. That is, it asks for analogues of the roots of unity, as complex numbers that are particular values of the exponential function; the requirement is that such numbers should generate a whole family of further number fields that are analogues of the cyclotomic fields and their subfields.The classical theory of complex multiplication, now often known as the Kronecker Jugendtraum, does this for the case of any imaginary quadratic field, by using modular functions and elliptic functions chosen with a particular period lattice related to the field in question. Goro Shimura extended this to CM fields. The general case is still open as of 2014. Leopold Kronecker described the complex multiplication issue as his liebster Jugendtraum or “dearest dream of his youth”.".
- Hilberts_twelfth_problem wikiPageExternalLink smf_sem-cong_3_243-273.html.
- Hilberts_twelfth_problem wikiPageExternalLink jugend-ps.pdf.
- Hilberts_twelfth_problem wikiPageID "2164726".
- Hilberts_twelfth_problem wikiPageLength "8416".
- Hilberts_twelfth_problem wikiPageOutDegree "58".
- Hilberts_twelfth_problem wikiPageRevisionID "664108026".
- Hilberts_twelfth_problem wikiPageWikiLink Abelian_extension.
- Hilberts_twelfth_problem wikiPageWikiLink Abelian_group.
- Hilberts_twelfth_problem wikiPageWikiLink Abelian_variety_of_CM-type.
- Hilberts_twelfth_problem wikiPageWikiLink Algebraic_number_field.
- Hilberts_twelfth_problem wikiPageWikiLink Algebraic_number_theory.
- Hilberts_twelfth_problem wikiPageWikiLink American_Mathematical_Society.
- Hilberts_twelfth_problem wikiPageWikiLink CM-field.
- Hilberts_twelfth_problem wikiPageWikiLink Carl_Friedrich_Gauss.
- Hilberts_twelfth_problem wikiPageWikiLink Category:Algebraic_number_theory.
- Hilberts_twelfth_problem wikiPageWikiLink Category:Conjectures.
- Hilberts_twelfth_problem wikiPageWikiLink Category:Hilberts_problems.
- Hilberts_twelfth_problem wikiPageWikiLink Class_field_theory.
- Hilberts_twelfth_problem wikiPageWikiLink Complex_multiplication.
- Hilberts_twelfth_problem wikiPageWikiLink Cyclotomic_field.
- Hilberts_twelfth_problem wikiPageWikiLink David_Hilbert.
- Hilberts_twelfth_problem wikiPageWikiLink Elliptic_function.
- Hilberts_twelfth_problem wikiPageWikiLink Emil_Artin.
- Hilberts_twelfth_problem wikiPageWikiLink Exponential_function.
- Hilberts_twelfth_problem wikiPageWikiLink Fundamental_pair_of_periods.
- Hilberts_twelfth_problem wikiPageWikiLink Galois_group.
- Hilberts_twelfth_problem wikiPageWikiLink Galois_module.
- Hilberts_twelfth_problem wikiPageWikiLink Goro_Shimura.
- Hilberts_twelfth_problem wikiPageWikiLink Group_(mathematics).
- Hilberts_twelfth_problem wikiPageWikiLink Harold_Stark.
- Hilberts_twelfth_problem wikiPageWikiLink Hasse–Weil_zeta_function.
- Hilberts_twelfth_problem wikiPageWikiLink Hilbert_class_field.
- Hilberts_twelfth_problem wikiPageWikiLink Hilbert_modular_form.
- Hilberts_twelfth_problem wikiPageWikiLink Hilberts_problems.
- Hilberts_twelfth_problem wikiPageWikiLink Kronecker–Weber_theorem.
- Hilberts_twelfth_problem wikiPageWikiLink Kummer_theory.
- Hilberts_twelfth_problem wikiPageWikiLink L-function.
- Hilberts_twelfth_problem wikiPageWikiLink Langlands_program.
- Hilberts_twelfth_problem wikiPageWikiLink Leopold_Kronecker.
- Hilberts_twelfth_problem wikiPageWikiLink Modular_form.
- Hilberts_twelfth_problem wikiPageWikiLink Quadratic_field.
- Hilberts_twelfth_problem wikiPageWikiLink Rational_number.
- Hilberts_twelfth_problem wikiPageWikiLink Robert_Langlands.
- Hilberts_twelfth_problem wikiPageWikiLink Root_of_unity.
- Hilberts_twelfth_problem wikiPageWikiLink Shimura_variety.
- Hilberts_twelfth_problem wikiPageWikiLink Société_mathématique_de_France.
- Hilberts_twelfth_problem wikiPageWikiLink Stark_conjectures.
- Hilberts_twelfth_problem wikiPageWikiLink Tate_module.
- Hilberts_twelfth_problem wikiPageWikiLink Yutaka_Taniyama.
- Hilberts_twelfth_problem wikiPageWikiLink Étale_cohomology.
- Hilberts_twelfth_problem wikiPageWikiLink Évariste_Galois.
- Hilberts_twelfth_problem wikiPageWikiLinkText "12th".
- Hilberts_twelfth_problem wikiPageWikiLinkText "Hilbert's Twelfth Problem".
- Hilberts_twelfth_problem wikiPageWikiLinkText "Hilbert's twelfth problem".
- Hilberts_twelfth_problem align "right".
- Hilberts_twelfth_problem source "Kronecker in a letter to Dedekind in 1880 reproduced in volume V of his collected works, page 455".
- Hilberts_twelfth_problem width "33.0".
- Hilberts_twelfth_problem wikiPageUsesTemplate Template:As_of.
- Hilberts_twelfth_problem wikiPageUsesTemplate Template:Cite_book.
- Hilberts_twelfth_problem wikiPageUsesTemplate Template:Harvs.
- Hilberts_twelfth_problem wikiPageUsesTemplate Template:Hilberts_problems.
- Hilberts_twelfth_problem wikiPageUsesTemplate Template:Quotebox.
- Hilberts_twelfth_problem wikiPageUsesTemplate Template:Reflist.
- Hilberts_twelfth_problem subject Category:Algebraic_number_theory.
- Hilberts_twelfth_problem subject Category:Conjectures.
- Hilberts_twelfth_problem subject Category:Hilberts_problems.
- Hilberts_twelfth_problem hypernym Extension.
- Hilberts_twelfth_problem type Software.
- Hilberts_twelfth_problem type Conjecture.
- Hilberts_twelfth_problem type Statement.
- Hilberts_twelfth_problem type Statement.
- Hilberts_twelfth_problem comment "Kronecker's Jugendtraum or Hilbert's twelfth problem, of the 23 mathematical Hilbert problems, is the extension of the Kronecker–Weber theorem on abelian extensions of the rational numbers, to any base number field.".
- Hilberts_twelfth_problem label "Hilbert's twelfth problem".
- Hilberts_twelfth_problem sameAs Q1093498.
- Hilberts_twelfth_problem sameAs Kronecker_Jugendtraum.
- Hilberts_twelfth_problem sameAs ヒルベルトの第12問題.
- Hilberts_twelfth_problem sameAs Décimo_segundo_problema_de_Hilbert.
- Hilberts_twelfth_problem sameAs m.06rn7_.
- Hilberts_twelfth_problem sameAs Hilberts_tolfte_problem.
- Hilberts_twelfth_problem sameAs Q1093498.
- Hilberts_twelfth_problem sameAs 希爾伯特第十二問題.
- Hilberts_twelfth_problem wasDerivedFrom Hilberts_twelfth_problem?oldid=664108026.
- Hilberts_twelfth_problem isPrimaryTopicOf Hilberts_twelfth_problem.