Higher solutions of hypergeometric systems and Dwork cohomology (Q1296437)
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scientific article; zbMATH DE number 1319601
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Higher solutions of hypergeometric systems and Dwork cohomology |
scientific article; zbMATH DE number 1319601 |
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Higher solutions of hypergeometric systems and Dwork cohomology (English)
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8 March 2000
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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.
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\(D\)-modules
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hypergeometric functions
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monomials
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hypergeometric differential module
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Dwork cohomology
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