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

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

2003-09-26

arxiv.org/abs/cs/0309050v1

Computer Science

Symbolic Computation

To appear in The Journal of Integer Sequences

Scientific paper

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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