Multivariate Davenport series

Arnaud Durand (1) , Stéphane Jaffard (2)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay
2 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

We consider series of the form $\sum a_n \{n\cdot x\}$, where $n\in\Z^{d}$ 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.

Mots clés: Davenport series; multifractal analysis; pointwise regularity; Sobolev regularity; Hausdorff dimension; sets with large intersection

Domaines: Théorie des nombres [math.NT]; Analyse classique [math.CA]; Analyse fonctionnelle [math.FA]

Arnaud Durand, Stéphane Jaffard. Multivariate Davenport series. 2012. ⟨hal-00696089⟩