Families of lattices from cyclic extensions of Q

02/23/2016 - 12:15pm
02/23/2016 - 1:10pm
Carmelo Interlando (San Diego State University)

Let F/Q be a cyclic extension of degree p, an odd unramified prime in F/Q. As usual, let O_F be the ring of integers of F. The derivation of the trace form on F/Q will be discussed, followed by a method to determine its minimum in certain sub-modules of O_F. The method will then yield an algorithm for optimizing the choice of the modules, ultimately leading to families of dense p-dimensional lattices. Several numerical examples will be provided.

Millikan 2099, Pomona College