  The space-borne missions CoRoT and Kepler have provided seismic data of
unprecedented quality. Among the observed stars, red giants show a complex
oscillation pattern exhibiting pressure modes as well as mixed modes. The
latter carry information on the radiative region properties of these stars. The
very high precision of Kepler data provide enough accuracy to decipher the
complex structure of the mixed-mode pattern and, therefore, deduce precise
information on the structure of the stellar core. In this work, we studied the
precise influence of the core structural discontinuities on the mixed-mode
pattern. These phenomena have indeed an influence on the gravity waves that
propagate inside the core of the star and, therefore, on the mixed-mode
pattern. In this study, we aim to investigate the impact of core structural
discontinuities on the observed mixed-mode pattern and measure their properties
for several red giants. We identified several objects showing evidence of
deviations in their mixed-mode frequency pattern that are characteristic of
core structural discontinuities. We fitted these deviations and showed that
they likely correspond to the influence of the inner convective core of these
stars.
