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In this memoir, we study the even unimodular lattices of rank at most 24, aswell as a related collection of automorphic forms of the orthogonal, symplecticand linear groups of small rank. Our guide is the question of determining thenumber of p-neighborhoods, in the sense of M. Kneser, between two isometryclasses of such lattices. We prove a formula for this number, in which occurcertain Siegel modular forms of genus 1 and 2. It has several applications,such as the proof of a conjecture of G. Nebe and B. Venkov about the linearspan of the higher genus theta series of the Niemeier lattices, the computationof the p-neighborhoods graphs of the Niemeier lattices (the case p = 2 beingdue to Borcherds), or the proof of a congruence conjectured by G. Harder.Classical arguments reduce the problem to the description of the automorphicrepresentations of a suitable integral form of the Euclidean orthogonal groupof R^24 which are unramified at each finite prime and trivial at thearchimedean prime. The recent results of J. Arthur suggest several newapproaches to this type of questions. This is the other main theme that wedevelop in this memoir. We give a number of other applications, for instance tothe classification of Siegel modular cuspforms of weight at most 12 for thefull Siegel modular group.

Formes automorphes et voisins de Kneser des r\'eseaux de Niemeier