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Quantitative weak approximation of rational points on quadrics

组织者

刁晗生 , 胡悦科 , 埃马纽埃尔·勒库图里耶 , 凯撒·鲁普

演讲者

黄治中

时间

2022年11月15日 16:00 至 17:00

地点

Tsinghua-Ningzhai-W11

线上

Zoom 293 812 9202 (BIMSA)

摘要

The classical Hasse—Minkowski theorem states that rational points on quadrics (if non-empty) satisfy weak approximation. We explain how Heath-Brown’s delta circle method allows to obtain a quantitive and effective version of this theorem, namely counting rational points of bounded height on quadrics satisfying prescribed local conditions with optimal error terms. We then discuss applications in intrinsic Diophantine approximation on quadrics. This is based on joint work in progress with M. Kaesberg, D. Schindler, A. Shut.