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Results of a leptonic jet model for the prompt emission and early afterglowsof GRBs are presented. The synchrotron component is modeled with the canonicalBand spectrum and the synchrotron self-Compton component is calculated from theimplied synchrotron-emitting electron spectrum in a relativistic plasma blob.In the comoving frame the magnetic field is assumed to be tangled and theelectron and photon distributions are assumed to be isotropic. TheCompton-scattered spectrum is calculated using the full Compton cross-sectionin the Thomson through Klein-Nishina using the Jones formula. Pair productionphotoabsorption, both from ambient radiation in the jet and from theextragalactic background light (EBL), is taken into account. Results arepresented as a function of a small set of parameters: the Doppler factor, theobserved variability timescale, the comoving magnetic field, the peaksynchrotron flux, and the redshift of the burst. Model predictions will betested by multiwavelength observations, including the {\em Swift} and {\emGLAST} satellites, which will provide unprecedented coverage of GRBs.

Nonthermal Synchrotron and Synchrotron Self-Compton Emission from GRBs: Predictions for {\em Swift} and {\em GLAST}