Diophantine Inequalities and Quasi-algebraically Closed Fields
نویسندگان
چکیده
Consider a form g(x1, . . . , xs) of degree d, having coefficients in the completion Fq((1/t)) of the field of fractions Fq(t) associated to the finite field Fq. We establish that whenever s > d, then the form g takes arbitrarily small values for non-zero arguments x ∈ Fq[t ]. We provide related results for problems involving distribution modulo Fq[t ], and analogous conclusions for quasi-algebraically closed fields in general.
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