Prime numbers and factorization of polynomials

Autor:	Singh, Jitender
Rok vydání:	2024
Předmět:	Mathematics - Number Theory Mathematics - Algebraic Geometry 11R09 12J25 12E05 11C08
Druh dokumentu:	Working Paper
Popis:	In this article, we obtain upper bounds on the number of irreducible factors of some classes of polynomials having integer coefficients, which in particular yield some of the well known irreducibility criteria. For devising our results, we use the information about prime factorization of the values taken by such polynomials at sufficiently large integer arguments along with the information about their root location in the complex plane. Further, these techniques are extended to bivariate polynomials over arbitrary fields using non-Archimedean absolute values, yielding extensions of the irreducibility results of M. Ram Murty and S. Weintraub to bivariate polynomials. Comment: 11 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2411.18366 Zobrazit plný text záznamu View this record from Arxiv