On page 263 of this book review appears the following:

Given the centrality of L-functions to the Langlands program, nothing would seem more natural (than a presentation of elementary algebraic number theory from the standpoint of L-functions and their analytic properties), but in fact the properties of L-functions traditionally of interest to analytic number theorists - for example, the location of zeroes in the critical strip (the Generalized Riemann Hypothesis) - have historically had little to do with the preoccupations of the Langlands program. Thanks largely to the efforts of a few charismatic and determined individuals, this is beginning to change and Langlands himself has in recent years turned to methods in analytic number theory in an attempt to get beyond the visible limits of the techniques developed over the last few decades.

I'd like to ask for a big picture exposition of how such questions about the location of zeroes of L-functions appear and interact with the Langlands program. My interest is mainly cultural and the answer should be tailored for the outsider to number theory (I'm viewing Langlands program algebraically as the pursuit of a nonabelian class field theory.)

A more crude question is:

Does the Langlands program say anything about the Grand Riemann Hypothesis or vice versa?

This is almost certainly too crude a question for MO, but Langlands seems to have such an amazing unifying appeal, that I feel a temptation to see how much it subsumes. I fully expect an answer like "It is impossible to coherently discuss this without years of training". Thank you for any attempt to explain things to someone who is not a number theorist, in advance!

holomorphy. $\endgroup$ – Chandan Singh Dalawat Jan 19 '13 at 14:082more comments