The fluxes of atmospheric muons and neutrinos are calculated by a three dimensional Monte Carlo simulation with the air shower code CORSIKA using the hadronic interaction models DPMJET, VENUS, GHEISHA, and UrQMD. For the simulation of low energy primary particles the original CORSIKA has been extended by a parametrization of the solar modulation and a microscopic calculation of the directional dependence of the geomagnetic cut-off functions. An accurate description for the geography of the Earth has been included by a digital elevation model, tables for the local magnetic field in the atmosphere, and various atmospheric models for different geographic latitudes and annual seasons. CORSIKA is used to calculate atmospheric muon fluxes for different locations and the neutrino fluxes for Kamioka. The results of CORSIKA for the muon fluxes are verified by an extensive comparison with recent measurements. The obtained neutrino fluxes are compared with other calculations and the influence of the hadronic interaction model, the geomagnetic cut-off and the local magnetic field on the neutrino fluxes is investigated.
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