Computing Igusa's local zeta functions of univariate polynomials, and linear feedback shift registers
| dc.creator | Zúñiga-Galindo, W. A. | |
| dc.date | 2002-04-16 | |
| dc.date.accessioned | 2026-07-07T04:48:10Z | |
| dc.date.available | 2026-07-07T04:48:10Z | |
| dc.description | In this paper we present a polynomial time algorithm to compute the local zeta function Z(s,f) attached to a polynomial f(x) in Z[x] (in one variable, with splitting field Q) and a prime p. The algorithm reduces in polynomial time the computation of Z(s,f) to the computation of a factorization of f(x) over Q. This reduction is accomplished by constructing a weighted tree from the p-adic expansion of the roots of f(x) modulo a certain power of p, and then associating a generating function to this tree. The generating function constructed in this way coincides with the local zeta function of f(x). We also propose a new class of candidates for one-way functions based on Igusa's zeta functions attached to polynomials in one variable. | |
| dc.identifier | https://arxiv.org/abs/math/0204360 | |
| dc.identifier | http://arxiv.org/abs/math/0204360 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63945 | |
| dc.subject | Number Theory | |
| dc.title | Computing Igusa's local zeta functions of univariate polynomials, and linear feedback shift registers | |
| dc.type | text |