Asymptotic formulas for the logarithm of general L-functions at and near s=1

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.