Values of inhomogeneous forms at S‐integral points. Issue 2 (16th April 2022)

• Record Type: Journal Article
• Authors: Ghosh, Anish; Han, Jiyoung
• Is Part Of: Mathematika. Volume 68:Issue 2(2022)
• Page Start: 565
• Page End: 593
• Publication Date: 2022-04-16
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.1112/mtk.12137
• Languages: English
• ISSNs: 0025-5793

Abstract

Abstract: We prove effective versions of Oppenheim's conjecture for generic inhomogeneous forms in the S ‐arithmetic setting. We prove an effective result for fixed rational shifts and generic forms and we also prove a result where both the quadratic form and the shift are allowed to vary. In order to do so, we prove analogues of Rogers' moment formulae for S ‐arithmetic congruence quotients as well as for the space of affine lattices. We believe the latter results to be of independent interest.