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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.

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  • $\begingroup$ Many thanks to all users, for the care and attention to improve the posts of this site. $\endgroup$
    – user142929
    Aug 24, 2019 at 20:56
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    $\begingroup$ Please make your questions self-contained. It's a lot to ask of volunteer helpers to go find, translate, and read an entire paper to understand what you are asking about. $\endgroup$ Aug 25, 2019 at 18:04
  • $\begingroup$ I add the link gaceta.rsme.es/abrir.php?id=1275 many thanks @GregMartin to you and Mr. Myerson $\endgroup$
    – user142929
    Aug 25, 2019 at 18:07
  • $\begingroup$ I'm voting to close this question because it is in effect asking for open-ended teaching/tutoring $\endgroup$
    – Yemon Choi
    Sep 1, 2019 at 13:18
  • $\begingroup$ With all due respect @YemonChoi I am asking about a different example of geometrical interpretation for a different particular values of a Dirichlet series. For example imagine that I can ask about an interpretation for $|G_k|$, where $G_k$ are the Gregory coefficients in the spirit of the article William J. Keith, Sequences of density $\zeta(k)-1$, INTEGERS: Electronic Journal of Combinatorial Number Theory 10 #A19 10 (2010). Then I am asking about an interpretation, if possible in a different scenario, I mean an example. Any case I say I'm sorry to you. $\endgroup$
    – user142929
    Sep 1, 2019 at 17:43

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