Restricted Successive Minima

Abstract

We give bounds on the successive minima of an $o$-symmetric convex body under the restriction that the lattice points realizing the successive minima are not contained in a collection of forbidden sublattices. Our investigations extend former results to forbidden full-dimensional lattices, to all successive minima and complement former results in the lower dimensional case.

11 pages, Abstract and Introduction revised in view of new added references

References in corpus (1)

• A Blichfeldt-type inequality for centrally symmetric convex bodies

Cited by in corpus (2)

• On the covering radius of lattice zonotopes and its relation to view-obstructions and the lonely runner conjecture
• Diophantine avoidance and small-height primitive elements in ideals of number fields