Additive Energy and the Hausdorff dimension of the exceptional set in metric pair correlation problems

Christoph Aistleitner, Gerhard Larcher, Mark Lewko

For a sequence of integers $\{a(x){\}}_{x\ge 1}$ we show that the distribution of the pair correlations of the fractional parts of $\{⟨\alpha a(x)⟩{\}}_{x\ge 1}$ is asymp…