The Norm Index Theorem (An Analytic Proof)

TL;DR

This paper provides an analytic proof of the norm index theorem for cyclic extensions of number fields, utilizing spectral theory of the idele class group to establish the result.

Contribution

It introduces an analytic proof of the norm index theorem, offering a new approach compared to traditional algebraic methods.

Findings

Proves the norm index theorem using spectral theory.

Establishes a connection between spectral theory and number field extensions.

Provides a new perspective on class field theory.

Abstract

We give an analytic proof of the norm index theorem $[I_:K^* N(I_L)] =[L:K]$ for cyclic extensions of number fields using spectral theory of the idele class group.