Automorphic Forms on Feit’s Hermitian Lattices

Codes over rings, complex lattices and Hermitian modular forms

We introduce the finite ring S2m = Z2m + iZ2m . We develop a theory of self-dual codes over this ring and relate self-dual codes over this ring to complex unimodular lattices. We describe a theory of shadows for these codes and lattices. We construct a gray map from this ring to the ring Z2m and relate codes over these rings, giving special attention to the case when m = 2. We construct various...

Introductory lectures on automorphic forms

1 Orbital integrals and the Harish-Chandra transform. This section is devoted to a rapid review of some of the basic analysis that is necessary in representation theory and the basic theory of automorphic forms. Even though the material below looks complicated it is just the tip of the iceberg. 1.1 Left invariant measures. Let X be a locally compact topological space with a countable basis for ...

Automorphic Forms

We apply a theorem of J. Lurie to produce cohomology theories associated to certain Shimura varieties of type U(1, n−1). These cohomology theories of topological automorphic forms (TAF ) are related to Shimura varieties in the same way that TMF is related to the moduli space of elliptic curves. We study the cohomology operations on these theories, and relate them to certain Hecke algebras. We c...

Automorphic Forms on Shimura Varieties

Automorphic forms on GL(2)

For us it is imperative not to consider functions on the upper half plane but rather to consider functions on GL(2,Q)\GL(2,A(Q)) where A(Q) is the adéle ring of Q. We also replace Q by an arbitrary number field or function field (in one variable over a finite field) F . One can introduce [3] a space of functions, called automorphic forms, and the notion that an irreducible representation π ofGL...