Ghosh, Anish ; Han, Jiyoung (2021) Values of Inhomogeneous Forms at S-integral points arXiv.org.
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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.
Item Type: | Other |
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Source: | Copyright of this article belongs to author(s). |
ID Code: | 123699 |
Deposited On: | 11 Oct 2021 11:28 |
Last Modified: | 11 Oct 2021 11:28 |
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