Measurements of the neutral current cross sections for deep inelastic scattering in e− p collisions at HERA with a longitudinally polarised electron beam are presented. The single-differential cross-sections dσ/dQ 2, dσ/dx and dσ/dy and the double-differential cross sections in Q2 and x are measured in the kinematic region y <0.9 and Q2 > 185 GeV2 for both positively and negatively polarised electron beams and for each polarisation state separately. The measurements are based on an integrated luminosity of 169.9 pb −1 taken with the ZEUS detector in 2005 and 2006 at a centre-of-mass energy of 318 GeV. The structure functions and are determined by combining the e− p results presented in this paper with previously measured e+ p neutral current data. The asymmetry parameter A− is used to demonstrate the parity violating effects of electroweak interactions at large spacelike photon virtuality. The measurements agree well with the predictions of the Standard Mode
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