# Simplest case of Langlands-Shahidi method

I would like to read the simplest examples of Langlands-Shahidi method carried out to prove the functional equation of $L$-function.

Could the constant term of $\mathrm{GL}(2)$-Eisenstein series be used to prove the functional equation of $L$-functions? (standard on $\mathrm{GL}(2)$ or Rankin-Selberg on $\mathrm{GL}(2) \times \mathrm{GL}(2)$ or adjoint/symmetric square on $\mathrm{GL}(2)$)

It includes a detailed exposition of the $\mathrm{GL}(2)×\mathrm{GL}(2)$ case, from both the Langlands-Shahidi and the Rankin-Selberg point of view (and the relation between them). Of course, general $\mathrm{GL}(n)×\mathrm{GL}(m)$ and symmetric powers are also treated.