Remarks on the pair correlation statistic of Kronecker sequences and lattice point counting

Abstract In this short note, we reformulate the task of calculating pair correlation statistics a Kronecker sequence as lattice point counting problem. This can be done analogously to based approach which was used (re-)prove famous three gap property for sequences. We show that recently developed techniques then applied derive certain class sequences have $$\beta $$ ? -pair correlations all $$0< \beta < 1$$ 0 < 1 .