TITLE: Langlands' original observation about Ramanujan conjecture
QUESTION [12 upvotes]: Obviously functoriality of arbitrary high symmetric power lifts of automorphic forms on GL(2) will lead to the Ramanujan conjecture. But I guess that is too strong for Ramanujan. I came across some statement online some months back that Langlands observed something much weaker(but still about symmetric powers) will also imply Ramanujan conjecture. 
What's Langlands' original observation?

REPLY [5 votes]: Aurel has already given a good answer to this, and as I note in my comment to his answer one needs only the holomorphy of $L(s,\pi, \text{sym}^k)$ in the region Re$(s)>1$ to obtain the Ramanujan conjecture.  The argument is described in Section 8 of Langlands's paper: Problems in the theory of automorphic forms.