Local-global Principle for Integers from Thin Subgroups of SL2(Z[i])

讲座时间 Datetime: 

星期二, 2020/11/03 - 从 11:00 到 14:00

地点 Venue: 

海琴2号A457会议室

报告人 Speaker: 

肖玄玄 助理教授

单位 Affiliation: 

澳门科技大学

报告摘要 Abstract: 

Let Gamma\subset SL2(Z[i]) be a finitely generated Gaussian thin subgroup and w; v be primitive vectors in Z^4-{0}. We study the orbit S = {<\rho(\gamma)w,v>:gamma\in\Gamma} with a homomorphism \rho: SL2(C) \to SO_F®. Using Hardy-Littlewood circle method and some infinite co-volume lattice point counting techniques developed by Bourgain, Kontorovich and Sarnak, together with Gamburds 5=6 spectral gap, we show that if the critical exponent \delta of \Gamma is sufficiently close to 2, then a density-one subset of all admissible integers (i.e. integers passing all local obstructions) are actually in S with a power savings on the size of the exceptional set (i.e. the set of admissible integers failing to appear in S). This is joint work with Xin ZHANG (HKU).