  We consider a general form of L-function L(s) defined by an Euler product and
satisfies several analytic assumptions. We show several asymptotic formulas for
L(1) and log L(1). In particular those asymptotic formulas are valid for
Dirichlet L-functions attached to almost all Dirichlet characters. Our theorems
should be compared with former results due to Elliott, Montgomery and
Weinberger, etc.
