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arXiv · 1711.05673

Counting factorisations of monomials over rings of integers modulo $N$

Jonathan Hickman·James Wright
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Abstract

A sharp bound is obtained for the number of ways to express the monomial $X^n$ as a product of linear factors over $\mathbb{Z}/p^α\mathbb{Z}$. 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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Jonathan Hickman, James Wright. 2017-11-15. Counting factorisations of monomials over rings of integers modulo $N$. https://arxiv.org/abs/1711.05673

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