Solvability of Planar Complex Vector Fields with Homogeneous   Singularities
  In this paper we study the equation $Lu=f$, where $L$ is a $\C$-valued vector field in $\R^2$ with a homogeneous singularity. The properties of the solutions are linked to the number theoretic properties of a pair of complex numbers attached to the vector field. 
Abdelhamid Meziani
math.AP