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.
Jayadev Athreya, Assistant Professor, Director, Illinois Geometry Lab, Department of Mathematics, University of Illinois
"Apollonian Circle Packings and the Riemann Hypothesis,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 16
, Article 13.
Available at: http://scholar.rose-hulman.edu/rhumj/vol16/iss2/13