Few months ago I found in arXiv a remarkable paper that the author shares as [1]. In those days I read such paper and I tried understand the more possible. To me these lecture notes are a precious didactic resource at the researcher level.
Today I wondered what could be the more relevant facts that one find in those figures or charts with what the author illustrated his explanation, on assumption that (here we consider $\text{Im}(s)>0$, where $s$ is the complex variable) the Riemann Hypothesis fails (you can consider the scenarios more relevant, but I am interested mainly in the scenario concerning to that there are two simple zeros with different real parts on the critical strip).
Question. I would like to know the more remarkable facts of the X-ray (see [1]) of $\zeta(s)$, or closely related functions (like its first derivative $\zeta'(s)$, the Dirichlet Eta function...), on assumption that the Riemann Hypothesis fails, as companion of [1]. Thus I am asking about speculative figures (you can add also reasonings with mathematical formulas) explaining in the spirit of [1], if it is possible, the most remarkable anomalies that one hope to find in similar figures for the Riemann Zeta function (or, if you need it in your explanation, in related functions to the Riemann Zeta function). Many thanks.
You can then add yourself drafted figures.
References:
Currently you can find next article as arXiv:math/0309433 on arXiv
[1] J. Arias-de-Reyna, X-Ray of Riemann's zeta-function. Universidad de Sevilla (2003).