A Spherical Maximal Function Along the Primes

Dr. Theresa Anderson
University of Wisconsin-Madison
NSF PostDoc

“Many problems at the interface of analysis and number theory involve showing that the primes, though deterministic, exhibit random behavior. The Green-Tao theorem stating that the primes contain infinitely long arithmetic progressions is one such example. In this talk, we show that prime vectors equidistribute on the sphere in the same manner as a random set of integer vectors would be expected to. We further quantify this via connecting classical tools from harmonic analysis with analytic number theory. This is joint work with Cook, Hughes, and Kumchev, and should be accessible to graduate students in all disciplines.”