On the $\sigma$-Pair Correlation Density of Quadratic Sequences Modulo One

Thomas Hille

In this note we study the $\sigma$-pair correlation density \begin{equation*}R_2^σ([a,b], \{ θ_n \}_n, N)= \frac{1}{N^{2-σ}} \# \big \{ 1 \leq j \neq k \leq N \, \big| \, θ_{j} - θ_{k}…