Apollonian Circle Packings and the Riemann Hypothesis

Authors

Jason Hempstead, University of Washington

Abstract

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.

Faculty Sponsor

Jayadev Athreya

Recommended Citation

Hempstead, Jason (2015) "Apollonian Circle Packings and the Riemann Hypothesis," Rose-Hulman Undergraduate Mathematics Journal: Vol. 16: Iss. 2, Article 13.
Available at: https://scholar.rose-hulman.edu/rhumj/vol16/iss2/13