On Incomplete Distance Sets in Z p ⇥
نویسنده
چکیده
In this paper we discuss the Erdős-Falconer distance problem. The classical Erdős distance problem in R, d 2, asks for the smallest possible size of (E) = {|x y| : x, y 2 E} with E ⇢ R a finite set. An analogous problem is the Falconer distance problem which asks how large does the Hausdor↵ dimension of a compact set E ⇢ R, d 2, needs to be to ensure that the Lebesgue measure of (E), defined as above, is positive. The Erdős-Falconer distance problem in Z2
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