Joint Weighted Limit Theorems for General Dirichlet Series

Abstract

In the paper,two joint weighted limit theorems in the sense of weak convergence of probability measures on the complex plane for general Dirichlet series are obtained. The first of them gives only the existence of the limit measure, while in the second theorem,under some additional hypothesis on the weight function, the explicit form of the limit measure is presented. Namely, the limit measure coincides with the distribution of some random element related to considered Dirichlet series.

Keywords:

• General Dirichlet series
• joint limit theorem
• probability measure
• weak con vergence
• weighted limit theorem

AMS Subject Classification:

• 11M41