Recently I have been reading Automorphic Representations and $L$-Functions for the General Linear Group: Volume I by D. Goldfeld and J. Hundley.
On page 51 there is a remark by Ivan Fesenko:
So, the most fundamental theorems of classical algebraic number theory follow as easy and fast corollaries of the adelic computation of the zeta function.
Before this sentence, it is shown how one can obtain the classical functional equation for the Riemann zeta function by computing the adelic integral of certain test functions using the adelic Poisson summation formula. The remark says that it is possible to do this over any number field $K$, and the corresponding functional equation implies, e.g., Dirichlet's unit theorem follows easily from this.
Where can I find proofs of these? How does one prove classical results in number theory (e.g. Dirichle's unit theorem) by automorphic forms? Any books or articles?
Thanks in advance!