On Diophantine properties for convergence of formal solutions (Q1079729)

The author presents a theorem which gives a necessary and sufficient criterion for the convergence of all formal solutions of a partial differential equation \(P(x;\partial)u=f(x)x^{\omega}\), (\(\omega\in {\mathbb{C}}\), f analytic), in two variables \(x_ 1,x_ 2\). The short note also contains some remarks and two corollaries, but for details the author refers to a preprint of another paper.