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- Hilbert's_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”.".
- Hilbert's_twelfth_problem wikiPageExternalLink smf_sem-cong_3_243-273.html.
- Hilbert's_twelfth_problem wikiPageExternalLink jugend-ps.pdf.
- Hilbert's_twelfth_problem wikiPageID "2164726".
- Hilbert's_twelfth_problem wikiPageRevisionID "605483732".
- Hilbert's_twelfth_problem align "right".
- Hilbert's_twelfth_problem hasPhotoCollection Hilbert's_twelfth_problem.
- Hilbert's_twelfth_problem source "Kronecker in a letter to Dedekind in 1880 reproduced in volume V of his collected works, page 455".
- Hilbert's_twelfth_problem width "33.0".
- Hilbert's_twelfth_problem subject Category:Algebraic_number_theory.
- Hilbert's_twelfth_problem subject Category:Conjectures.
- Hilbert's_twelfth_problem subject Category:Hilbert's_problems.
- Hilbert's_twelfth_problem type Abstraction100002137.
- Hilbert's_twelfth_problem type Attribute100024264.
- Hilbert's_twelfth_problem type Cognition100023271.
- Hilbert's_twelfth_problem type Concept105835747.
- Hilbert's_twelfth_problem type Condition113920835.
- Hilbert's_twelfth_problem type Conjectures.
- Hilbert's_twelfth_problem type Content105809192.
- Hilbert's_twelfth_problem type Difficulty114408086.
- Hilbert's_twelfth_problem type Hilbert'sProblems.
- Hilbert's_twelfth_problem type Hypothesis105888929.
- Hilbert's_twelfth_problem type Idea105833840.
- Hilbert's_twelfth_problem type Problem114410605.
- Hilbert's_twelfth_problem type PsychologicalFeature100023100.
- Hilbert's_twelfth_problem type Speculation105891783.
- Hilbert's_twelfth_problem type State100024720.
- Hilbert's_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.".
- Hilbert's_twelfth_problem label "Hilbert's twelfth problem".
- Hilbert's_twelfth_problem label "Kronecker Jugendtraum".
- Hilbert's_twelfth_problem label "ヒルベルトの第12問題".
- Hilbert's_twelfth_problem sameAs Kronecker_Jugendtraum.
- Hilbert's_twelfth_problem sameAs ヒルベルトの第12問題.
- Hilbert's_twelfth_problem sameAs m.06rn7_.
- Hilbert's_twelfth_problem sameAs Q15933072.
- Hilbert's_twelfth_problem sameAs Q15933072.
- Hilbert's_twelfth_problem sameAs Hilbert's_twelfth_problem.
- Hilbert's_twelfth_problem wasDerivedFrom Hilbert's_twelfth_problem?oldid=605483732.
- Hilbert's_twelfth_problem isPrimaryTopicOf Hilbert's_twelfth_problem.