Take the tour ×  I've been learning about Dedekind zeta
functions and some basic L-functions in my introductory
algebraic number theory class, and I've been wondering why some
functions are called L-functions and others are called zeta
functions. I know that the zeta function is a product of
L-functions, so it seems like an L-function is somehow a
component of a zeta function (at least in the case of Artin
L-functions, they correspond to specific representations). Is
this the idea behind the distinction between "zeta function" and
"L-function"? How do things generalize to other kinds of zeta-
and L-functions?  share|improve this question Currently, I feel
like there is no consensus among the answers, with Hansen's and
Buzzard's answers reflecting one view, and engelbrekt and Will
Sawin's reflecting another. –  David Corwin Nov 14 '12 at 18:08
It is likely that "all are true", I think... as in my add-on
answer below. –  paul garrett Nov 14 '12 at 19:00 There is a
reason that Prof. Nick Katz's course this semes