Effective Density for Inhomogeneous Quadratic Forms II: Fixed Forms and Generic Shifts

Anish Ghosh, Dubi Kelmer, Shucheng Yu

Type: Article

Publication Date: 2023-08-17

Citations: 0

DOI: https://doi.org/10.1093/imrn/rnad192

Abstract

Abstract 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 previous paper [13] 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 $(T)$.

Locations

International Mathematics Research Notices - View
arXiv (Cornell University) - View - PDF

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