We approach the analytic side of class field theory with more limited objectives than usual, with only the intention of seeing why classical class field theory could not remain “purely algebraic” (assuming this was desirable). Since the modern analytic methods have become so diffuse from the classical standpoint, the present chapter, unlike earlier ones, cannot be reasonably taken to be a motivation for contemporary developments in the analytic theory.
KeywordsPrime Ideal Class Number Class Field Quadratic Field Abelian Extension
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