Counting factorisations of monomials over rings of integers modulo $N$
作者: Jonathan HickmanJames 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 polynomialsCongruence equationsIgusa 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.
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关键词翻译
关键词翻译
  • 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