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Configurations in fractal sets in Euclidean and non-Archimedean local fields : [errata] Fraser, Robert 2018

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33426-errata_2018_may_fraser_robert.pdf [ 26.08kB ]
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ErrataOriginal Document: “Configurations in Fractal Sets in Euclidean and Non-Archimedean Local Fields”Link: Robert Fraser***Begin errata.Page 4: Theorem 1.2.1: Replace with the following:Let {fℓ} : Rnvℓ → R be a countable family of nonzero polynomials of degreeat most d with integer coefficients, where R = Zp or Fq[[t]]. If R = Fpf [[t]]for some prime p, then assume in addition that d < p. Then there exists aset E ⊂ Rn of Hausdorff dimension ndand Minkowski dimension n such that,for all ℓ, the set E does not contain vℓ distinct points x1, . . . , xvℓ such thatfℓ(x1, . . . , xvℓ) = 0.Page 73: Case 1, Theorem 1.2.1 or 1.2.2: replace the second sentence withthe following.In the case of Theorem 1.2.2, we have by assumption that |∂αf | is nonzero onall of T1×· · ·×Tv for an appropriate multi-index α. In the case of Theorem 1.2.1,we use the fact that f is a polynomial. On Zp, any polynomial of any degree dhas some partial derivative of order d that is equal to a nonzero constant. Thesame holds for Fpf [[t]] if we make the additional assumption that d < p.1


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