THE DENSITY OF INTEGRAL POINTS ON COMPLETE INTERSECTIONS

In this paper, an upper bound for the number of integral points of bounded height on an affine complete intersection defined over ℤ is proven. The proof uses an extension to complete intersections of the method used for hypersurfaces by Heath-Brown (The density of rational points on non-singular hypersurfaces, Proc. Indian Acad. Sci. Math. Sci. 104 (1994) 13–29), the so called ‘q-analogue’ of van der Corput's AB process.