Special Values of L-functions

In the last chapter, we studied the analytic properties of L-functions, in particular their zero distributions. If we simply regard an L-function as a complex analytic function, then its values at different points seem to be equally important or unimportant. However, since our L-functions all come from arithmetic geometric or automorphic origins, it turns out that the function values at certain points are more transparent in revealing the associated arithmetic or automorphic information, and thus deserve special attention. It is for this reason that such L-function values are called special values.