Abstract
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 language | English (US) |
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Pages (from-to) | 1941-1944 |
Number of pages | 4 |
Journal | Proceedings of the American Mathematical Society |
Volume | 125 |
Issue number | 7 |
DOIs | |
State | Published - 1997 |
Externally published | Yes |