Strombergsson, Andreas and Vishe, Pankaj (2020) 'An effective equidistribution result for SL(2,R)\ltimes (R^2)^{oplus k} and application to inhomogeneous quadratic forms.', Journal of the London Mathematical Society., 102 (1). pp. 143-204.
Abstract
Let G = SL(2, R) (R2) ⊕k and let Γ be a congruence subgroup of SL(2, Z) (Z2) ⊕k. We prove a polynomially effective asymptotic equidistribution result for special types of unipotent orbits in Γ\G which project to pieces of closed horocycles in SL(2, Z)\ SL(2, R). As an application, we prove an effective quantitative Oppenheim-type result for the quadratic form (m1 − α) 2 + (m2 − β) 2 − (m3 − α) 2 − (m4 − β) 2, for (α, β) ∈ R2 of Diophantine type, following the approach by Marklof [Ann. of Math. 158 (2003) 419–471] using theta sums.
| Item Type: | Article |
|---|---|
| Full text: | Publisher-imposed embargo (AM) Accepted Manuscript File format - PDF (1316Kb) |
| Full text: | Publisher-imposed embargo (VoR) Version of Record Available under License - Creative Commons Attribution. File format - PDF (Advance online version) (850Kb) |
| Full text: | (VoR) Version of Record Available under License - Creative Commons Attribution. Download PDF (850Kb) |
| Status: | Peer-reviewed |
| Publisher Web site: | https://doi.org/10.1112/jlms.12316 |
| Publisher statement: | © 2020 The Authors. The Journal of the London Mathematical Society is copyright © London Mathematical Society. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. |
| Date accepted: | 02 March 2020 |
| Date deposited: | 24 March 2020 |
| Date of first online publication: | 07 April 2020 |
| Date first made open access: | 11 April 2020 |
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