The distribution of primes and an introduction to class field theory
We will consider several situations in which the primes of a number field are mapped in a natural way into a finite abelian group. In each case they turn out to be distributed uniformly (in some sense) among the members of the group; in particular each group element is the image of infinitely many primes. Except in certain special cases, however, the proof of this depends upon facts from class field theory which will not be proved in this book. Thus this chapter provides an introduction and motivation for class field theory, which is the study of the abelian extensions of a number field, by showing how the existence of certain extensions leads to uniform distribution results.
KeywordsGalois Group Number Field Class Field Abelian Extension Finite Abelian Group
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