5 papers
The -Trace System
Daniel Barlet
We study a simple 1-parameter perturbation of the regular holonomic Trace System satisfied by a complex power of the root of the universal polynomial of degree k as a holomorphic f…
Generalized Brieskorn Modules I: Convergent (a,b)-modules
Daniel Barlet
This paper is the first one of two papers whose goal is to give a converse to the main result of my previous paper [6], so to prove the existence of multiple poles for the distribu…
Generalized Brieskorn Modules III. The algebra
Daniel Barlet
In this paper we introduce and study the ''convergent'' algebra (containing ''a'' and ''b'' and acting on holomorphic germs in ''a'') which naturally acts on the ''generalized Brie…
Generalized Brieskorn Modules II: Higher Bernstein Polynomials and Multiple Poles
Daniel Barlet
Our main result is to show that the existence of a root in. ----Nfor the p-th Bernstein polynomial of the (a,b)-module generated by a holomorphicform in the (convergent) Briesk…
On Symmetric and Anti-symmetric Partial Differential Operators
Daniel Barlet
We study the action of symmetric PDO on the module of anti-symmetric functions in . We show that over the Weyl algebra of the elementary symmetric functions, this…