A generic effective Oppenheim theorem for systems of forms
نویسندگان
چکیده
We prove a uniform effective density theorem as well an counting result for generic system comprising polynomial with mild homogeneous condition and several linear forms using Rogers' second moment formula the Siegel transform on space of unimodular lattices.
منابع مشابه
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Let Qi, i = 1, . . . , t, be real nondegenerate indefinite quadratic forms in d variables. We investigate under what conditions the closure of the set {(Q1(x̄), . . . , Qt(x̄)): x̄ ∈ Zd − {0̄}} contains (0, . . . , 0). As a corollary, we deduce several results on the magnitude of the set ∆ of g ∈ GL(d,R) such that the closure of the set {(Q1(gx̄), . . . , Qt(gx̄)) : x̄ ∈ Zd − {0̄}} contains (0, . . . ,...
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Let Qi, i = 1, . . . , t, be real nondegenerate indefinite quadratic forms in d variables. We investigate under what conditions the closure of the set {(Q1(x̄), . . . , Qt(x̄)): x̄ ∈ Zd − {0̄}} contains (0, . . . , 0). As a corollary, we deduce several results on the magnitude of the set ∆ of g ∈ GL(d,R) such that the closure of the set {(Q1(gx̄), . . . , Qt(gx̄)) : x̄ ∈ Zd − {0̄}} contains (0, . . . ,...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2021
ISSN: ['0022-314X', '1096-1658']
DOI: https://doi.org/10.1016/j.jnt.2020.07.002