In this paper, we describe how one can state the Riemann hypothesis in terms of a geometric problem about Apollonian circle packings. We use, as a black box, results of Zagier, and describe numerical experiments which were used in a recent paper by Athreya, Cobeli, and Zaharescu.
"Apollonian Circle Packings and the Riemann Hypothesis,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 16:
2, Article 13.
Available at: https://scholar.rose-hulman.edu/rhumj/vol16/iss2/13