  The prompt emission spectrum of Gamma-ray bursts (GRB) is characterized by a
smoothly joint broken power-law spectrum known as the Band function. The
typical low-energy photon index is $\sim -1$, which poses challenge to the
standard synchrotron radiation models. We investigate the electron energy
spectrum as a result of the interplay among adiabatic stochastic acceleration
(ASA), particle injection, and synchrotron cooling. In the ASA-dominated
low-energy range, ASA enables an efficient hardening of the injected energy
spectrum to approach a spectral index $-1$. In the synchrotron
cooling-dominated high-energy range, the injected high-energy electrons undergo
fast synchrotron cooling and have a softer photon spectrum. With the energy
range of the injected electrons broadly covering both the ASA- and synchrotron
cooling-dominated ranges, the resulting photon number spectrum has the low- and
high-energy indices as $\alpha_s \sim -1$ and $\beta_s \sim -p/2-1$,
respectively. The break energy is of the order of $\sim 100 $ keV, depending on
the turbulence properties.
