Higher solutions of hypergeometric systems and Dwork cohomology
Some new results on hypergeometric functions and rings generated by monomials are given. First, a resolution of the hypergeometric differential module \(M_a\) (associated to the \(N\)-variable Weyl algebra) is constructed. This enables to obtain higher formal and analytic solutions of \(M_a\). Then, a connection between these solutions and the algebraic Dwork cohomology (of de Rham-type) is established. By standard results in the theory of \(D\)-modules, it is proven that the Dwork cohomology is finite dimensional.
scientific article; zbMATH DE number 1319601