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

W. A. Zuniga-Galindo
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Abstract

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.

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W. A. Zuniga-Galindo. 2003-09-26. Computing Igusa's Local Zeta Functions of Univariate Polynomials, and Linear Feedback Shift Registers. https://arxiv.org/abs/cs/0309050

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