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We present observations of 10 type Ia supernovae (SNe Ia) between 0.16 < z <0.62. With previous data from our High-Z Supernova Search Team, this expandedset of 16 high-redshift supernovae and 34 nearby supernovae are used to placeconstraints on the Hubble constant (H_0), the mass density (Omega_M), thecosmological constant (Omega_Lambda), the deceleration parameter (q_0), and thedynamical age of the Universe (t_0). The distances of the high-redshift SNe Iaare, on average, 10% to 15% farther than expected in a low mass density(Omega_M=0.2) Universe without a cosmological constant. Different light curvefitting methods, SN Ia subsamples, and prior constraints unanimously favoreternally expanding models with positive cosmological constant (i.e.,Omega_Lambda > 0) and a current acceleration of the expansion (i.e., q_0 < 0).With no prior constraint on mass density other than Omega_M > 0, thespectroscopically confirmed SNe Ia are consistent with q_0 <0 at the 2.8 sigmaand 3.9 sigma confidence levels, and with Omega_Lambda >0 at the 3.0 sigma and4.0 sigma confidence levels, for two fitting methods respectively. Fixing a``minimal'' mass density, Omega_M=0.2, results in the weakest detection,Omega_Lambda>0 at the 3.0 sigma confidence level. For a flat-Universe prior(Omega_M+Omega_Lambda=1), the spectroscopically confirmed SNe Ia requireOmega_Lambda >0 at 7 sigma and 9 sigma level for the two fitting methods. AUniverse closed by ordinary matter (i.e., Omega_M=1) is ruled out at the 7sigma to 8 sigma level. We estimate the size of systematic errors, includingevolution, extinction, sample selection bias, local flows, gravitationallensing, and sample contamination. Presently, none of these effects reconcilesthe data with Omega_Lambda=0 and q_0 > 0.Comment: 36 pages, 13 figures, 3 table files Accepted to the Astronomical  Journa

Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant