We present an analytical study of the effect of small convective cores on the oscillations of solar-like pulsators. Based on an asymptotic analysis of the wave equation near the center of the star, we derive an expression for the perturbations to the frequencies of radial modes generated by a convective core and discuss how these perturbations depend on the properties of the core. Moreover, we propose a diagnostic tool to isolate the predicted signature of the core, constructed from a particular combination of the oscillation frequencies, and we validate this tool with simulated data. We also show that the proposed tool can be applied to the pulsation data soon expected from satellite missions such as CoRoT and Kepler to constrain the amplitude of the discontinuity in the sound speed at the edge of the convective core, the ratio between the sound speed and the radius at this same location, and the stellar age.
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