Quadratic forms in 8 prime variables

by Prof. Ben Green (University of Oxford)

Thursday, May 5, 2022 from 16:00 to 17:00 (Asia/Kolkata)
at Via Zoom

Description

Abstract: I will discuss a recent paper of mine, the aim of which is to
count the number of prime solutions to Q(p_1,..,p_8) = N, for a fixed
quadratic form Q and varying N. The traditional approach to problems of
this type, the Hardy-Littlewood circle method, does not quite suffice. The
main new idea is to involve the Weil representation of the symplectic
groups Sp_8(Z/qZ). I will explain what this is, and what it has to do with
the original problem. I hope to make the talk accessible to a fairly
general audience.