Values of Inhomogeneous Forms at S-integral points

Ghosh, Anish ; Han, Jiyoung (2021) Values of Inhomogeneous Forms at S-integral points

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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.

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Deposited On:11 Oct 2021 11:28
Last Modified:11 Oct 2021 11:28

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