Multivariate davenport series

Abstract

We consider series of the form ∑an{n · x}, where n ∈ Zd and {x} is the sawtooth function. They are the natural multivariate extension of Davenport series. Their global (Sobolev) and pointwise regularity are studied and their multifractal properties are derived. Finally, we list some open problems which concern the study of these series.