Simultaneous distribution of fractional parts of Riemann zeta zeros

We investigate the simultaneous distribution of the fractional parts of $\{{\alpha }_1\gamma ,{\alpha }_2\gamma ,\cdots ,{\alpha }_n\gamma \}$, where $n\ge 2$, ${\alpha }_1$, ${\alpha }_2$, $\dots$, ${\alpha }_n$ are fixed, distinct positive real numbers and $\gamma$ runs over the imaginary parts of the non-trivial zeros of the Riemann zeta-function.