A residue calculus approach to the uniform Artin-Rees lemma

The uniform Artin-Rees lemma has been proved by C. Huneke using algebraic methods. We give a new proof for this result in the analytic setting, using residue calculus and a method involving complexes of Hermitian vector bundles. We also have to introduce a type of product of complexes of vector bundles, which may be applicable in the solution of other division problems with respect to product ideals.