Counting factorisations of monomials over rings of integers modulo N

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Abstract

A sharp bound is obtained for the number of ways to express the monomial Xn as a product of linear factors over Z/pαZ. 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.
Original languageEnglish
Article number1
Pages (from-to)255-282
Number of pages28
JournalJournal de Théorie des Nombres
Volume31
Early online date29 Jul 2019
DOIs
Publication statusE-pub ahead of print - 29 Jul 2019

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