论文标题
不均匀二次形式的有效密度II：固定形式和通用偏移
Effective density for inhomogeneous quadratic forms II: fixed forms and generic shifts
论文作者
论文摘要
我们建立了Oppenheim对通用不均匀二次形式的猜想的有效版本。我们证明了固定二次形式和通用偏移的结果。我们的结果补充了我们的同伴论文，我们考虑了通用形式和固定的偏移。在本文中，我们使用奇异定理，尤其是我们建立了一个较强的光谱差距，具有有效界限的正交群体的某些表示，这些差异不具有Kazhdan的性质（T）。
We establish effective versions of Oppenheim's conjecture for generic inhomogeneous quadratic forms. We prove such results for fixed quadratic forms and generic shifts. Our results complement our companion paper where we considered generic forms and fixed shifts. In this paper, we use ergodic theorems and in particular we establish a strong spectral gap with effective bounds for some representations of orthogonal groups which do not possess Kazhdan's property (T).
