Limit Theorems

In this chapter, we prove a limit theorem dealing with weakly convergent probability measures for L-functions from the class S in the space of analytic functions. Throughout this chapter, we assume that L ∈ S. We remark that we will not make use of axiom (v), so the results hold in a more general context; however, with respect to later applications, there is no need to introduce a further class. We follow the presentation of Laurinčikas [187, 188] (functions in S form a subclass of Matsumoto zeta-functions considered herein). Besides, we refer the interested reader to Laurinčikas' survey [185] and his monograph [186].