Abstract:

The study of the number of lattice points in dilated regions has a long history, with several outstanding open problems. In this lecture, I will describe a new variant of the problem, in which we study the distribution of lattice points with prime coordinates. We count lattice points in which both coordinates are prime, suitably weighted, which lie in the dilate of a convex planar domain having smooth boundary, with nowhere vanishing curvature. We obtain an asymptotic formula, with the main term being the area of the dilated domain, and our goal is to study the remainder term. Assuming the Riemann Hypothesis, we give a sharp upper bound, and further assuming that the positive imaginary parts of the zeros of the Riemann zeta functions are linearly independent over the rationals allows us to give a formula for the value distribution function of the properly normalized remainder term. Time permitting, I will explain some background motivation coming from Quantum Chaos.(joint work with Bingrong Huang)

Brief Introduction to the Presenter:

Zeev Rudnick (Tel Aviv University)

Inviter:

Huang Bingrong

Time:

15:00-16:00, April 27 (Monday)

Location:

the Zoom meeting  ID:635 813 7757

Sponsored by: School of Mathematics, Shandong University