On bernstein-sato polynomials

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We show that for fixed n and d the set of Bernstein-Sato polynomials of all the polynomials in at most n variables of degrees at most d is finite. As a corollary, we show that there exists an integer t depending only on n and d such that f-t generates Rf as a module over the ring of the k-linear differential operators of R, where k is an arbitrary field of characteristic 0, R is the ring of polynomials in n variables over k and f ∈ R is an arbitrary non-zero polynomial of degree at most d.

Original languageEnglish (US)
Pages (from-to)1941-1944
Number of pages4
JournalProceedings of the American Mathematical Society
Issue number7
StatePublished - 1997


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