  We present a systematic analysis of the spectral and temporal properties of
17 GRBs co-detected by GBM and LAT on board the Fermi satellite by May 2010. We
performed a time-resolved spectral analysis of all the bursts with the finest
temporal resolution allowed by statistics, in order to avoid temporal smearing
of different spectral components. We found that the time-resolved spectra of 14
out of 17 GRBs are best modeled with the Band function over the entire Fermi
spectral range, which may suggest a common origin for emissions detected by LAT
and GBM. GRB 090902B and GRB 090510 require the superposition between an MeV
component and an extra power law component, with the former having a sharp
cutoff above E_p. For GRB 090902B, this MeV component becomes progressively
narrower as the time bin gets smaller, and can be fit with a Planck function as
the time bin becomes small enough. In general, we speculate that
phenomenologically there may be three elemental spectral components : (I) a
Band-function component (e.g. in GRB 080916C) that extends in a wide energy
range and does not narrow with reducing time bins, which may be of the
non-thermal origin; (II) a quasi-thermal component (e.g. in GRB 090902B) with
the spectra progressively narrowing with reducing time bins; and (III) another
non-thermal power law component extending to high energies. The spectra of
different bursts may be decomposed into one or more of these elemental
components. We compare this sample with the BATSE sample and investigate some
correlations among spectral parameters. We discuss the physical implications of
the data analysis results for GRB prompt emission, including jet compositions
(matter-dominated vs. Poynting-flux-dominated outflow), emission sites
(internal shock, external shock or photosphere), as well as radiation
mechanisms (synchrotron, synchrotron self-Compton, or thermal Compton
upscattering).
