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Counting factorisations of monomials over rings of integers modulo $N$. (arXiv:1711.05673v1 [math.NT])
来源于:arXiv
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. 查看全文>>