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

We obtain an asymptotic formula for the sum \(H=\sum_{0<\gamma_k\le T,\,1\le k\le 4}h(\gamma_1+\gamma_2-\gamma_3-\gamma_4),\) 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 \(L^1(\mathbb R)\) .