I put this as a gentle question with the aim to get an answer from an informative point of view, because I am curious about it. You can, however, also add references that will be answered as a reference request, or add your conclusions / arguments. You consider it useful for your colleagues.

In the past I have known the following theories about the hypothesis known as Lindelöf and its relation to the Riemann Hypothesis (I have read them from different sources and for different audiences, but I find it difficult and I understand only excerpts) and on the other hand a phenomenon , which is known as the universality of Riemann's zeta function.

See the Wikipedia *Lindelof hypothesis* respectively. *Zeta function universality*,

I also know about the zeta function of the Ramanujan

$$ varphi (s) = sum_ {n = 1} ^ infty frac { tau (n)} {n ^ s} $$

or also known as Ramanujan tau Dirichlet series, see article *Tau Dirichlet series* from the encyclopedia Wolfram MathWorld. And from an informative point of view the articles (1) and *Lecture X* from (2).

**Question.** A) Does Ramanujan's zeta function fulfill a similar Lindelöf hypothesis? I ask if it is possible / possible to write a similar expression for Ramanujan's Dirichlet-L series instead of the Riemann zeta function. B) Also, I would like to know if the phenomenon of universality makes sense for the zeta function of Ramanujan (tell us a similar statement)

similar to the set of Voroni of 1975. **Many thanks.**

As I ask as curiosity, if the literature answer is a reference request, I try to search for it and read it from the literature. If my questions have no mathematical meaning or there is no motivation to study such things, please explain why.

## references:

(1) Carlos Julio Moreno, *A necessary and sufficient condition for the Riemann hypothesis for Ramanujan's zeta function*Illinois J. Math., Vol. 18, Issue 1 (1974), 107-114.

(2) G.H. Hardy, *Twelve lectures on topics from his life and work*, AMS Chelsea Publishing (2002).