# Generalized Dirichlet Series

I am looking into Dirichlet series book by Mandelbrojt but unfortunately I don't find results regarding boundary behavior of the type of series $$\sum a_ne^{-\lambda_ns}$$ in which the density ($$\limsup n/\lambda_n$$) is not finite. The case I want some information about is $$n/\lambda_n^2 \rightarrow \alpha$$ and $$a_n$$ are integers. (so $$\{a_n\}$$ is not $$l_2$$ type) I couldn't find it among the works of Aleksei Leont'ev as well.