On the geometry of numbers of non-convex star-regions with hexagonal symmetry

Abstract

A method of Mordell is applied to the study of critical determinants and critical lattices of a type of two-dimensional star-domains which can be roughly described as that of regions similar to | r3sin 36| ^ 8c3. In part I three general theorems are proved. They are applied in part II to obtain the critical determinants and all the critical lattices of some special regions of this type.