  We aim at reproducing the chemical evolution of the bulge of M31 by means of
a detailed chemical evolution model, including radial gas flows coming from the
disk. We study the impact of the initial mass function, the star formation rate
and the time scale for bulge formation on the metallicity distribution function
of stars. We compute several models of chemical evolution using the metallicity
distribution of dwarf stars as an observational constraint for the bulge of
M31. Then, by means of the model which best reproduces the metallicity
distribution function, we predict the [X/Fe] vs. [Fe/H] relations for several
chemical elements (O, Mg, Si, Ca, C, N). Our best model for the bulge of M31 is
obtained by means of a robust statistical method and assumes a Salpeter initial
mass function, a Schmidt-Kennicutt law for star formation with an exponent
k=1.5, an efficiency of star formation of $\sim 15\pm 0.27\, Gyr^{-1}$, and an
infall timescale of $\sim 0.10\pm 0.03$Gyr. Our results suggest that the bulge
of M31 formed very quickly by means of an intense star formation rate and an
initial mass function flatter than in the solar vicinity but similar to that
inferred for the Milky Way bulge. The [$\alpha$/Fe] ratios in the stars of the
bulge of M31 should be high for most of the [Fe/H] range, as is observed in the
Milky Way bulge. These predictions await future data to be proven.
