Sur la mesure spectrale de certaines suites arithmétiques

— Let S be thé family of complex séquences a = (a (n)} such that for every integer m, thé limit lim^^ ^L^Na(>Ooc(n+m) =y(m) N : exists. According to thé Bochner-Herglotz représentation theorem, there exists a bounded positive measure A such that y (m) = exp 2 i K mx dA (x). JR/Z Thé object of this article is to study thé relationship between thé behavior of thé séquence a and thé properties of thé measure A . Spécifie examples are discussed in détail which involve number theoritical methods. BULLETIN DE LA SOCIÉTÉ MATHÉMATIQUE DE FRANCE 24