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- W3207525829 abstract "We construct large Salem sets avoiding patterns, complementing previous constructions of pattern avoiding sets with large Hausdorff dimension. For a (possibly uncountable) family of uniformly Lipschitz functions ${ f_i : (mathbb{T}^d)^{n-2} to mathbb{T}^d }$, we obtain a Salem subset of $mathbb{T}^d$ with dimension $d/(n-1)$ avoiding nontrivial solutions to the equation $x_n - x_{n-1} = f_i(x_1,dots,x_{n-2})$. For a countable family of smooth functions ${ f_i : (mathbb{T}^d)^{n-1} to mathbb{T}^d }$ satisfying a modest geometric condition, we obtain a Salem subset of $mathbb{T}^d$ with dimension $d/(n-3/4)$ avoiding nontrivial solutions to the equation $x_n = f(x_1,dots,x_{n-1})$. For a set $Z subset mathbb{T}^{dn}$ which is the countable union of a family of sets, each with lower Minkowski dimension $s$, we obtain a Salem subset of $mathbb{T}^d$ of dimension $(dn - s)/(n - 1/2)$ whose Cartesian product does not intersect $Z$ except at points with non-distinct coordinates." @default.
- W3207525829 created "2021-10-25" @default.
- W3207525829 creator A5001373327 @default.
- W3207525829 date "2021-10-18" @default.
- W3207525829 modified "2023-09-27" @default.
- W3207525829 title "Large Salem Sets Avoiding Nonlinear Configurations." @default.
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