Скачать или смотреть Zeev Rudnick: Prime lattice points in ovals (NTWS 006)

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. (joint work with Bingrong Huang).

Number Theory Web Seminar: https://www.ntwebseminar.org

Original air date:
Thursday, May 21, 2020 (8am PDT, 11am EDT, 4pm BST, 5pm CEST, 8:30pm IST, 11pm China Standard Time)
Friday, May 22, 2020 (1am AEST, 3am NZST)