  Asteroseismology allows us to probe stellar interiors. Mixed modes can be
used to probe the physical conditions in red giant cores. However, we still
need to identify the physical mechanisms that transport angular momentum inside
red giants, leading to the slow-down observed for the red giant core rotation.
Thus large-scale measurements of the red giant core rotation are of prime
importance to obtain tighter constraints on the efficiency of the internal
angular momentum transport, and to study how this efficiency changes with
stellar parameters. This work aims at identifying the components of the
rotational multiplets for dipole mixed modes in a large number of red giant
oscillation spectra observed by Kepler. Such identification provides us with a
direct measurement of the red giant mean core rotation. We compute stretched
spectra that mimic the regular pattern of pure dipole gravity modes. Mixed
modes with same azimuthal order are expected to be almost equally spaced in
stretched period. The departure from this regular pattern allows us to
disentangle the various rotational components and therefore to determine the
mean core rotation rates of red giants. We obtained mean core rotation
measurements for 875 red giant branch stars. This large sample includes stars
with a mass as large as 2.5 $M_{\odot}$, allowing us to test the dependence of
the core slow-down rate on the stellar mass. This work on a large sample allows
us to refine previous measurements of the evolution of the mean core rotation
on the red giant branch. Rather than a slight slow down, our results suggest
rotation to be constant along the red giant branch, with values independent on
the mass.
