Counting factorisations of monomials over rings of integers modulo $N$
 作者： Jonathan Hickman,  James Wright 刊名： Journal de théorie des nombres de Bordeaux, 2019, Vol.31 (1), pp.255-282 来源数据库： The Center for Diffusion of Academic Mathematical Journals DOI： 10.5802/jtnb.1079 关键词： Factorising polynomials;  Congruence equations;  Igusa conjecture; 原始语种摘要： A sharp bound is obtained for the number of ways to express the monomial $X^n$ as a product of linear factors over $\mathbb{Z}/p^{\alpha }\mathbb{Z}$. The proof relies on an induction-on-scale procedure which is used to estimate the number of solutions to a certain system of polynomial congruences. The method also applies to more general systems of polynomial congruences that satisfy a non-degeneracy hypothesis.

• modulo
• rings　泥包
• conjecture　推测
• polynomial　多项式
• proof　证明
• satisfy　满足
• certain　确实的
• hypothesis　假说
• estimate　估计
• over　在上方