Automorphic Forms and Even Unimodular Lattices

This book includes a self-contained approach of the general theory of quadratic forms and integral Euclidean lattices, as well as a presentation of the theory of automorphic forms and Langlands' conjectures, ranging from the first definitions to the recent and deep classification results due to James Arthur. Its connecting thread is a question about lattices of rank 24: the problem of p -neighborhoods between Niemeier lattices. This question, whose expression is quite elementary, is in fact very