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BIMSA-YMSC Tsinghua Number Theory Seminar
Quantitative weak approximation of rational points on quadrics
Quantitative weak approximation of rational points on quadrics
Organizers
Hansheng Diao
, Yueke Hu
, Emmanuel Lecouturier
,
Cezar Lupu
Speaker
Zhizhong Huang
Time
Tuesday, November 15, 2022 4:00 PM - 5:00 PM
Venue
Tsinghua-Ningzhai-W11
Online
Zoom 293 812 9202
(BIMSA)
Abstract
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.