Recently for some class assignment we derived the functional equation of the Riemann zeta function and from that we deduced the zeroes of the zeta function together with its analytic continuation.
But my professor (as a side note) mentioned that the derivation of a functional equation is quite a deep property relating to L-Functions and modular forms i.e. https://mathoverflow.net/questions/2040/why-are-functional-equations-important.
However, some of the stuff he mentioned was quite complicated and I wonder if there are texts(books or notes) for recent graduates(basic background in complex-analysis, algebra so on.) that would be a good introduction to see how functional equations reveal important information regarding modular forms and so on.