Statistical Properties

Abstract

In this chapter we will consider the weak convergence of probability measures defined by terms of Lerch zeta-functions. We will prove one-dimensional and multidimensional limit theorems on the complex plane and in the space of analytic functions. Let, for T > 0,

$$\nu _T^\tau \left( \cdots \right) = \frac{1} {T}meas\left\{ {\tau \in \left[ {0,T} \right]: \ldots } \right\},$$

where instead of dots we write a condition satisfied by τ. Here meas A denotes the Lebesgue measure of the set A.