Equidistribution of quadratic roots and applications to prime number theory

Abstract: Given an irreducible quadratic polynomial of fixed discriminant, the quadratic roots mod $m$ are expected to be equidistributed as $m$ runs over reasonable sets. We will give a short historical survey on this topic, as well as our recent progress on the case of friable moduli. Moreover, a reasonable equidistribution can also lead to non-trivial multiplicative structures in prime number theory, and an application to a special case of Schinzel hypothesis will be discussed in this talk. The underlying tools will include Gauss’s correspondence in the theory of binary quadratic forms and arithmetic exponent pairs for trace functions developed by Jie Wu and the speaker.

Mathematics

Audience: researchers in the topic

ICCM 2020