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    Computing Igusa's Local Zeta Functions of Univariate Polynomials, and Linear Feedback Shift Registers

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    We give a polynomial time algorithm for computing the Igusa local zeta function Z(s,f)Z(s,f) attached to a polynomial f(x)\in \QTR{Bbb}{Z}[x], in one variable, with splitting field \QTR{Bbb}{Q}, and a prime number pp. We also propose a new class of Linear Feedback Shift Registers based on the computation of Igusa's local zeta function.Comment: To appear in The Journal of Integer Sequence
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