Deep-inelastic inclusive ep scattering at low x and a determination of \alpha_s

A precise measurement of the inclusive deep-inelastic scattering cross section is reported in the kinematic range GeV and . The data were recorded with the H1 detector at HERA in 1996 and 1997, and correspond to an integrated luminosity of 20 pb. The double differential cross section, from which the proton structure function and the longitudinal structure function are extracted, is measured with typically 1% statistical and 3% systematic uncertainties. The measured derivative is observed to rise continuously towards small x for fixed . The cross section data are combined with published H1 measurements at high for a next-to-leading order DGLAP QCD analysis. The H1 data determine the gluon momentum distribution in the range to within an experimental accuracy of about 3% for GeV. A fit of the H1 measurements and the data of the BCDMS collaboration allows the strong coupling constant and the gluon distribution to be simultaneously determined. A value of is obtained in NLO, with an additional theoretical uncertainty of about , mainly due to the uncertainty of the renormalisation scale. Received: 21 December 2000 / Revised version: 10 May 2001 / Published online: 6 July 2001