Date:

Mon, 06/06/202214:30-16:00

Title: Sectorial equidistribution of the roots of x^2=-1 mod p.

Abstract: The equation x2 + 1 = 0 mod p has solutions whenever p = 2 or 4n+1. A famous theorem of Fermat says that these primes are exactly the ones that can be described as a sum of two squares. That the roots of the former equation are equidistributed is a famous theorem of Duke, Friedlander and Iwaniec from 1995. We examine what happens to the distribution when one adds a restriction on the primes which has to do with the angle in the plane formed by their corresponding representation as a sum of squares. This simple arithmetic question has a solution which involves multiple disciplines of number theory, but the talk does not assume any previous background.

Abstract: The equation x2 + 1 = 0 mod p has solutions whenever p = 2 or 4n+1. A famous theorem of Fermat says that these primes are exactly the ones that can be described as a sum of two squares. That the roots of the former equation are equidistributed is a famous theorem of Duke, Friedlander and Iwaniec from 1995. We examine what happens to the distribution when one adds a restriction on the primes which has to do with the angle in the plane formed by their corresponding representation as a sum of squares. This simple arithmetic question has a solution which involves multiple disciplines of number theory, but the talk does not assume any previous background.