High Quality Content by WIKIPEDIA articles! Hilbert's twelfth problem, of the 23 Hilbert's problems, is the extension of Kronecker–Weber theorem on abelian extensions of the rational numbers, to any base number field. The classical theory of complex multiplication does this for any imaginary quadratic field. The more general cases, now often known as the Kronecker Jugendtraum (although not so accurately), are still open as of 2005. Leopold Kronecker is supposed to have described the complex multiplication issue as his liebster Jugendtraum or “dearest dream of his youth”.

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