Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Values of Inhomogeneous Forms at S-integral points   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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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: mtrl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga