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

We give a polynomial time algorithm for computing the Igusa local zeta function $Z(s,f)$ attached to a polynomial f(x)\in \QTR{Bbb}{Z}[x], in one variable, with splitting field \QTR{Bbb}{Q}, and a prime number $p$. 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