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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.

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