A Band function has become the standard spectral function used to describe the prompt emission spectra of gamma-ray bursts (GRBs). However, deviations from this function have previously been observed in GRBs detected by BATSE and in individual GRBs from the Fermi era. We present a systematic and rigorous search for spectral deviations from a Band function at low energies in a sample of the first two years of high fluence, long bursts detected by the Fermi Gamma-Ray Burst Monitor (GBM). The

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... e contains 45 bursts with a fluence greater than 2×10^-5 erg / cm^2 (10 - 1000 keV). An extrapolated fit method is used to search for low-energy spectral anomalies, whereby a Band function is fit above a variable low-energy threshold and then the best fit function is extrapolated to lower energy data. Deviations are quantified by examining residuals derived from the extrapolated function and the data and their significance is determined via comprehensive simulations which account for the instrument response. This method was employed for both time-integrated burst spectra and time-resolved bins defined by a signal to noise ratio of 25 σ and 50 σ. Significant deviations are evident in 3 bursts (GRB 081215A, GRB 090424 and GRB 090902B) in the time-integrated sample (∼ 7 GRB 090902B and GRB 090926A) in the time-resolved sample (∼ 11 advantage of the systematic, blind search analysis is that it can demonstrate the requirement for an additional spectral component without any prior knowledge of the nature of that extra component. Deviations are found in a large fraction of high fluence GRBs; fainter GRBs may not have sufficient statistics for deviations to be found using this method.