Effective Density for Inhomogeneous Quadratic Forms II: Fixed Forms and Generic Shifts-Reference-Cited by-同舟云学术

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

Published:2023-08-17 Issue:22 Volume:2023 Page:19507-19545
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Ghosh Anish¹,Kelmer Dubi²,Yu Shucheng³⁴

Affiliation:

1. School of Mathematics , Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India

2. Department of Mathematics , Boston College, Chestnut Hill, MA 02467-3806, USA

3. Department of Mathematics , Technion, Haifa, 3200003, Israel

4. School of Mathematical Sciences , University of Science and Technology of China (USTC), 230026, Hefei, China

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 $(T)$.

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

https://academic.oup.com/imrn/article-pdf/2023/22/19507/53636893/rnad192.pdf

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