  We study turbulence in the one-dimensional Burgers equation with a
white-in-time, Gaussian random force that has a Fourier-space spectrum $\sim
1/k$, where $k$ is the wave number. From very-high-resolution numerical
simulations, in the limit of vanishing viscosity, we find evidence for
multiscaling of velocity structure functions which cannot be falsified by
standard tests. We find a new artifact in which logarithmic corrections can
appear disguised as anomalous scaling and conclude that bifractal scaling is
likely.
