We present the results of a near-infrared imaging study of high redshift ( z \sim 3 ) quasars using the ESO-VLT .
Our targets were selected to have luminosities among the highest known ( absolute magnitude M _ { B } \la - 28 ) .
We searched for resolved structures underlying the bright point-source nuclei by comparing the QSO images with stars located in the same fields .
Two QSOs ( HE 2348 - 1444 at z = 2.904 and HE 2355 - 5457 at z = 2.933 ) are clearly resolved in K _ { \mathrm { s } } , and with somewhat lower significance also in H ; one object is resolved only in K _ { \mathrm { s } } .
At these redshifts , H and K _ { \mathrm { s } } correspond almost exactlly to rest-frame B and V , respectively , with virtually no K -correction .
We also report briefly the non-detection of some additional QSOs .
The detected host galaxies are extremely luminous with M _ { V } \sim - 25 .
Their rest-frame B - V colours , however , are close to zero in the Vega system , indicating substantial contributions from young stars and a stellar mass-to-light ratio below 1 ( in solar units ) .
Tentatively converting M _ { V } and B - V into rough estimates of stellar masses , we obtain values of M _ { \star } in the range of several 10 ^ { 11 } \ > M _ { \odot } , placing them within the high-mass range of recent high-redshift galaxy surveys .
We present optical spectra and use C iv line width measurements to predict virial black hole masses , obtaining typical values of { \bf M _ { \mathrm { bh } } \sim 5 \times 10 ^ { 9 } M _ { \odot } } .
With respect to the known correlation between host galaxy luminosity L _ { V, \mathrm { host } } and M _ { \mathrm { bh } } , our measurements reach to higher luminosities and redshifts than previous studies , but are completely consistent with them .
Comparing our objects with the local ( z \simeq 0 ) M _ { \mathrm { bh } } – M _ { \mathrm { bulge } } relation and taking also the low stellar mass-to-light ratios into account , we find tentative evidence for an excess in the M _ { \mathrm { bh } } / M _ { \mathrm { bulge } } mass ratio at z \sim 3 .