Let G = G(q) be a Chevalley group defined over a field Fq of characteristic 2. In this paper we determine the conjugacy classes of involutions in Aut(G) and the centralizers of these involutions. This study was begun in the context of a different problem.

Let H denote the complex upper half-plane and let η(z) denote Dedekind’s η-function

Soient N le noyau newtonien sur l’espace euclidien Rn à dimension n ≧ 3 et E l’espace de Banach formé par des fonctions finies et continues définies dans Rn s’annulant à l’infini et normé usuellement. Définissons l’opérateur de convolution K par Kf = –N*f. Dans cette note nous traitrons l’opérateur K dans E.

Let A be a real analytic set, M be a compact real analytic manifold and f : A × M → R be a real analytic function. Then we have a family of real analytic functions fa, a ∈ A, on M defined by fa(X) = f(a, x).

Let M and L be quadratic lattices over the maximal order of an algebraic number field. In case of dealing with representations of M by L, they sometimes assume certain indefiniteness and the condition rank L-rank M ≥ 3. In this case, representation problems are reduced not to global but to local problems by virtue of the strong approximation theorem for rotations and of the fact that for regular quadratic spaces U, V over a non-archimedian local field there is an isometry from U to V if dim V — dim U ≥ 3.

A holomorphic n × n-matric automorphic factor with respect to a lattice L in Cg means a system of holomorphic n × n-matrices {μα(z) | α ∈ L} such that