The remark [1] (in Spanish) shows a geometric interpretation (linking two sequences) of particular values of a given Dirichlet series, that are $\zeta(k)$ and $\zeta(2k)$. I wondered about if it is easy to show a geometric interpretation for a choice of particular values of a different Dirichlet series $\mathcal{D}(s)$. I am asking as curiosity to take/study another simple example, if possible.
Question. Please provide a geometrical interpretation of the particular values $\mathcal{D}(s_k)$ and/versus $\mathcal{D}(t_k)$, for a suitable Dirichlet series $\mathcal{D}(s)$ that you provide us, evaluating your example of Dirichlet series at the particular values $s_k$ and/or $t_k$, that are infinite sequences (you can take these sequences $a_k$ and $t_k$ as integers, real numbers or complex numbers, as you need in your construction). Many thanks.
As soon as possible (when there are some nice answers) I should to accept one.
References:
[1] Juan Luis Varona, Miniaturas matemáticas, La Gaceta de la RSME, Vol. 18 (2015), Núm. 2, Pág. 352.