On a Linear Form in the Ordinates of Zeros of the Riemann Zeta Function

We obtain an asymptotic formula for the sum
$$ H=\sum_{0<\gamma_k\leqslant T,\,1\leqslant k\leqslant 4}h(\gamma_1+\gamma_2-\gamma_3-\gamma_4), $$
where the $\gamma_k$ run over the imaginary parts of nontrivial zeros of the Riemann zeta function with multiplicities taken into account and the function $h$ belongs to some special class of functions in $L^1(\mathbb R)$.