Complex Multiplication
نویسنده
چکیده
Class field theory describes the abelian extensions of a number field using the arithmetic of that field. The Kronecker-Weber theorem states that all abelian extensions of the rationals are contained in cyclotomic fields. As we know, cyclotomic fields can be generated by special values of the exponential function e, and we call this the theory of complex multiplication for Gm. We would thus like to find other analytic functions whose special values generate abelian extensions of other number fields.
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