arXiv:1206.0493v4 [math.DS] 19 Dec 2014 GENERALIZED RIESZ PRODUCTS ON THE BOHR COMPACTIFICATION OF R (∗) E. H. EL ABDALAOUI Abstract. We study a class of generalized Riesz products connected to the spec- tral type of some class of rank one flows on R. Applying Kac’s central limit the- orem, we exhibit a large class of singular generalized Riesz products on the Bohr compactification of R. * Dedicated to Professors Jean-Paul Thouvenot and Bernard Host. revised version II. AMS Subject Classifications (2010) Primary: 42A05, 42A55; Secondary: 11L03, 42A61. Key words and phrases: Generalized Riesz products, almost periodic functions, Bohr compactification, mean value, Kac’s central limit theorem, Kakutani’s criterion, Bourgain’s singularity criterion, flat polynomials. 1