Pair Dependent Linear Statistics for Circular Beta Ensemble

We study limiting distribution of pair counting statistics of the form ${\sum }_{1\le i\mathrm{\ne }j\le N}f(L_N\text{*}({\theta }_i-{\theta }_j))$ for the circular $\beta$-ensemble (C$\beta$E) of random matrices for sufficiently smooth test function $f$ and $L_N=O(N)\mathrm{.}$ For $\beta =2$ and $L_N=N$ our results are inspired by a classical result of Montgomery on pair correlation of zeros of Riemann zeta function.