AERQS survey, limited by an exposure time $t_{\rm   
exp}\ge 300$ sec in the RASS-BSC [@vog99] and at high Galactic latitudes ($|b_{\rm gal}|\ge 30^{\circ}$).

The results on clustering reported in this paper are derived by scrambling the redshifts, and the right ascension ($RA$) and declination ($DEC$) coordinates for the total (AERQS) sample. The random $RA$ and $DEC$ are derived from Fig. \[areatot\], while the redshifts are randomly extracted from the observed (Gaussian smoothed) redshift distributions (Fig. \[histz\]).

In order to check the robustness of the results, we have carried out a more complex generation of random QSOs, which ensured the uniformity of the “synthetic” samples. The angular positions were chosen again randomly from the map in Fig. \[areatot\]. Then, for each object we generated random values for redshift and absolute magnitude reproducing the LF estimated by @LFC97 and @GC2000 in the redshift range $0.04\le z\le 2.2$. In particular for $\Phi   
(M_B,z)$ we adopt a double power-law relation evolving accordingly to a Luminosity Dependent Luminosity Evolution (LDLE) model:

$$\Phi (M_B,z)=   
{ {\Phi^\ast} \over { 10^{0.4[M_B-M_B^*(z)](\alpha + 1)} +   
10^{0.4[M_B-M_B^*(z)](\beta + 1)} } } \ , \\$$

where $$M_B^*(z) = M^*_B(z=2)-2.5 k \log [(1+z)/3]$$ and $$\begin{aligned}
\nonumber k = k_1 + k_2 [M_B-M_B^*(z)]e^{-{z/0.4}}&    
 