2002/04/16 by W. A. Zúñiga‐Galindo, W. A. Zúñiga-Galindo, Zúñiga-Galindo, W. A. · 1 citation
Computer Science · Engineering · Mathematics · #Cellular Automata and Applications #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT) #graph theory and CDMA systems #math.NT
paper · pdf · doi:10.48550/arxiv.math/0204360
arxiv created 2002/04/16 · openalex publication_date 2002/04/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.