数论研讨班：Almost prime points on unirational varieties

中科院数学与系统科学研究院

数学研究所

学术报告

数论研讨班

报告人：王玉超（上海大学）   

题  目：Almost prime points on unirational varieties

时  间：2023.07.11（星期二）14:30-16:30

地  点：数学院南楼N802

摘  要：In this talk, we generalise the definition of the saturation number introduced by Bourgain, Gamburd and Sarnak to investigate the distribution of rational points on unirational varieties whose coordinates have few prime factors. We prove that there exists an integer $r$ such that rational points for which the product of the coordinates has at most $r$ prime factors form a Zariski dense subset, provided that the variety has one rational point. Moreover, we may obtain rather small bounds for $r$ for several special cases. Our approach relies on the circle method, the weighted sieve and unirationality arguments.