APS
Speaker: Aratrika Pandey, IIT Bombay
Host: Ravi Raghunathan
Title: Simultaneous Khintchine theorem in local field of positive characteristic
Time, day and date: 11:45:00 AM – 12:45:00 PM, Wednesday, February 11
Venue: Ramanujan Hall
Abstract: In this talk, we focus on the convergence case of Khintchine's theorem for analytic nonplanar manifolds over local fields of positive characteristic, allowing general approximation functions $\psi$ that are not necessarily monotonic. Our approach is based on the method of counting rational points near manifolds developed by Beresnevich and Yang \cite{BY}. To address the scenario in which $\psi$ is not monotonic, we extend the function field by adjoining an appropriate root. Additionally, in the course of the proof, we establish several new results in the geometry of numbers over function fields, which we believe are of independent interest. If time permits, we will also briefly discuss the divergence case, which deals with lower bounds for counting rational points