On Smooth Ideals in Number Fields Original Research Article

For yset membership, variantimage>0an integral ideal of an algebraic number field image is calledy-smoothif the norms of all of its prime ideal factors are bounded byy. Assuming the generalized Riemann hypothesis we prove a lower bound for the numberψimage(x, y) of integraly-smooth ideals in image whose norms are bounded byxset membership, variantimage>0. Apart fromxandythis bound only depends on the degree of image.