Gowers uniformity of the primes in short intervals
Analysis and Geometry Seminar
8th May 2025, 3:00 pm – 4:00 pm
Fry Building, 2.04
The Gowers norms, introduced by Tim Gowers, are a way to measure the pseudorandomness properties of a set. In 2012, Green, Tao and Ziegler showed that the set of prime numbers is Gowers uniform, in the sense that a suitably normalised version of it has small Gowers norms. I will discuss a recent work where we show that the primes are Gowers uniform even when restricted to almost all short intervals of the form [x, x+x^c] for any constant c>1/3. I will also mention some applications that statements of this type have in ergodic theory and analytic number theory. This is based on joint work with Kaisa Matomäki, Maksym Radziwiłł, Xuancheng Shao and Terence Tao.
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