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A Spherical Maximal Function along the Primes

PDE and Applied Math Seminar

Speaker: Tess Anderson, University of Wisconsin
Location: 2112 MSB
Start time: Thu, Dec 7 2017, 4:10PM

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 with explicit bounds for naturally occurring maximal functions, which connects classical tools from harmonic analysis with analytic number theory. This is joint work with Cook, Hughes, and Kumchev.