Applications of Number Theory to Wireless Communcations: Units Groups, Quaternion Algebras, and Dedekind Zeta Functions

Research done by information theorists over the past decade has
shown that lattices constructed from rings of integers in number fields,
and orders in division algebras, provide codebooks well-suited for
communication over wireless channels.  In particular, recent work has shown
that when communication over a wireless channel occurs in the presence of
an eavesdropper, one can estimate the eavesdropper's probability of
correctly intercepting the message, using the regulator and Dedekind zeta
function of the underlying number field.  In this talk, we will explain
these basic concepts, and elaborate on ongoing work on wiretap channels.
 This is joint work with Camilla Hollanti and Emanuele Viterbo.