一、讲坛主题

Prime lattice points in ovals

二、主讲人

Zeev Rudnick

三、摘要

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)

四、主讲人简介

Zeev Rudnick (Tel Aviv University)

五、邀请人

黄炳荣

六、时间

4月27日（周一）15:00-16:00

七、讲座形式

加入Zoom会议，会议ID：635 813 7757

八、主办单位

山东大学数学学院