@misc{HenkSchymuraXue, author = {Henk, Martin and Schymura, Matthias and Xue, Fei}, title = {Packing minima and lattice points in convex bodies}, series = {Moscow Journal of Combinatorics and Number Theory}, volume = {10}, journal = {Moscow Journal of Combinatorics and Number Theory}, number = {1}, publisher = {Mathematical Sciences Publishers}, issn = {2640-7361}, doi = {10.2140/moscow.2021.10.25}, pages = {25 -- 48}, abstract = {Motivated by long-standing conjectures on the discretization of classical inequalities in the geometry of numbers, we investigate a new set of parameters, which we call packing minima, associated to a convex body K and a lattice Λ. These numbers interpolate between the successive minima of K and the inverse of the successive minima of the polar body of K and can be understood as packing counterparts to the covering minima of Kannan \& Lov{\´a}sz (1988). As our main results, we prove sharp inequalities that relate the volume and the number of lattice points in K to the sequence of packing minima. Moreover, we extend classical transference bounds and discuss a natural class of examples in detail.}, language = {en} }