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) attached to a polynomial f(x)∈ BbbZ[x], in one variable, with splitting field BbbQ, and a prime number p. We also propose a new class of Linear Feedback Shift Registers based on the computation of Igusa's local zeta function.