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.

Author Bio

Jason Hempstead performed the work presented as a part of the Illinois Geometry Lab (IGL) at the University of Illinois at Urbana Champaign, where he was a student studying physics and applied mathematics. He has since started graduate school in physics at the University of Washington.