On the density at integer points of a system comprising an inhomogeneous quadratic form and a linear form
نویسندگان
چکیده
We prove an analogue of the Oppenheim conjecture for a system comprising inhomogeneous quadratic form and linear in 3 variables using dynamics on space affine lattices.
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Oppenheim Conjecture for Pairs Consisting of a Linear Form and a Quadratic Form
Let Q be a nondegenerate quadratic form, and L is a nonzero linear form of dimension d > 3. As a generalization of the Oppenheim conjecture, we prove that the set {(Q(x), L(x)) : x ∈ Z} is dense in R provided that Q and L satisfy some natural conditions. The proof uses dynamics on homogeneous spaces of Lie groups.
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ژورنال
عنوان ژورنال: Mathematische Zeitschrift
سال: 2021
ISSN: ['1432-1823', '0025-5874']
DOI: https://doi.org/10.1007/s00209-021-02716-8