Tuesday 26 Sep 2017: Angles of Gaussian primes
Prof. Zeev Rudnick - Tel-Aviv University
Fermat showed that every prime p = 1 mod 4 is a sum of two squares: p = a^2+b^2, and hence such a prime gives rise to an angle whose tangent is the ratio b/a. Hecke showed, in 1919, that these angles are uniformly distributed, and uniform distribution in somewhat short arcs was given in by Kubilius in 1950 and refined since then. I will discuss the statistics of these angles on fine scales and present a conjecture, motivated by a random matrix model and by function field considerations.