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The Weil's zeta function (or local zeta function) in the Weil Conjectures for projective algebraic variety seems to appear in almost every exposition of the Langlands Conjectures.

Main Question:

I'm trying to figure out if there is a way to see the local zeta function as an Automorphic L-function in some properly established version of the Langlands Correspondence?

Comment:

I know the one reason Weil Conjectures appears in the discourse of Langlands is due to Ramanujan's Conjecture. I've been told that we can prove the Ramanujan's Conjecture by relating the normalised Hecke eigenform to some variety such that the eigenvalues appear in the local zeta function.

Now I read on pg 243 of An Introduction to the Langlands Program that: The Ramanujan-Petersson conjecture for GLn follows immediately from the Global Langlands Conjectures in characteristic p.

I don't know if this follows in a similar way as the Ramanujan Conjecture from the Weil Conjectures.

If I believe yes, then is the book suggesting that the Weil Conjectures can be considered a part of the Langlands Program, i.e., the Weil's Zeta function is an Automorphic L-function or similar??

I don't wanna be confusing somet

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Is the Weil's zeta function Automorphic?