... We report the results of a millimeter interferometric survey of compact 3 mm continuum sources in the inner 5.5'x5.5' region of the Serpens core. We detect 32 discrete sources above 4.0 mJy/beam, 21 of which are new detections at millimeter wavelengths. ... The mass spectrum of the clumps, dN/dM~M^(-2.1), is consistent with the stellar initial mass function, supporting the idea that the stellar masses in young clusters are determined by the fragmentation of turbulent cloud cores. ...