α n^d mod 1 exhibits Poissonian ℓ-point correlations for almost all α when d is large (depending on ℓ) and for a full-dimensional set of badly approximable α via determinant method counting and Fourier transference.
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Poissonian correlations of $\alpha n^d$ mod $1$
α n^d mod 1 exhibits Poissonian ℓ-point correlations for almost all α when d is large (depending on ℓ) and for a full-dimensional set of badly approximable α via determinant method counting and Fourier transference.