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Regular $$b$$-functions of $$D$$-modules. (English) Zbl 1160.32013
Summary: Let $$M$$ be an algebraic $$D$$-module defined on an affine space $$X$$ and $$Y$$ be a linear submanifold of $$X$$. We give an algorithm to determine if $$M$$ is regular specializable along $$Y$$, and to find, if so, its regular $$b$$-function. ($$M$$ has a regular $$b$$-function by definition if and only if $$M$$ is regular specializable.) We also prove that the $$A$$-hypergeometric system of Gelfand-Kapranov-Zelevinsky is always regular specializable along the origin.

##### MSC:
 32C38 Sheaves of differential operators and their modules, $$D$$-modules 33C70 Other hypergeometric functions and integrals in several variables 13P10 Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) 35N10 Overdetermined systems of PDEs with variable coefficients
SINGULAR; Kan
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