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Using the Echellete Spectrograph Imager (ESI) on the Keck II 10-m telescopewe have measured the redshifts of the host galaxies of gamma-ray bursts GRB990506 and GRB 000418, z=1.30658 +/- 0.00004 and 1.1181 +/- 0.0001,respectively. Thanks to the excellent spectral resolution of ESI we resolvedthe [O II] 3727 doublet in both cases. The measured redshift of GRB 990506 isthe highest known for a dark burst GRB, though entirely consistent with thenotion that dark and non-dark bursts have a common progenitor origin. Therelative strengths of the [O II], He I, [Ne III], and H gamma emission linessuggest that the host of GRB 000418 is a starburst galaxy, rather than a LINERor Seyfert 2. Since the host of GRB 000418 has been detected at sub-millimeterwavelengths these spectroscopic observations suggest that the sub-millimeteremission is due to star-formation (as opposed to AGN) activity. The [OII]-derived unobscured star-formation rates are 13 and 55 M_solar/yr for thehosts of GRB 990506 and GRB 000418, respectively. In contrast, thestar-formation rate of the host of GRB 000418 derived from sub-millimeterobservations is twenty times larger.Comment: To appear in the Astronomical Journal (accepted 4 December 2002). 15  pages, 3 Postscript figure

The Redshift Determination of GRB 990506 and GRB 000418 with the Echellete Spectrograph Imager on Keck