A new transfer principle in the geometry of numbers

Abstract

In my paper ( Proc. Roy. Soc. Edinburgh Sect. A 64 (1956), 223–238), I gave a general transfer principle in the geometry of numbers which consisted of inequalities linking the successive minima of a convex body in n dimensions with those of a convex body in N dimensions where in general N is greater than n. This result contained in particular my earlier theorem on compound convex bodies ( Proc. London Math. Soc. (3) 5 (1955), 358–379). In the present paper I apply essentially the same method to prove a new transfer principle which connects the successive minima of a convex body in m dimensions and those of a convex body in n dimensions with the successive minima of a convex body in mn dimensions.