Counting factorisations of monomials over rings of integers modulo N

Jonathan Hickman, James Wright

Type: Article

Publication Date: 2019-01-01

Citations: 1

DOI: https://doi.org/10.5802/jtnb.1079

Abstract

A sharp bound is obtained for the number of ways to express the monomial X n as a product of linear factors over ℤ/p α 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.

Locations

Journal de Théorie des Nombres de Bordeaux - View - PDF
arXiv (Cornell University) - View - PDF
Edinburgh Research Explorer (University of Edinburgh) - View - PDF
French digital mathematics library (Numdam) - View - PDF
Bordeaux Journal of Number Theory - View - PDF

Similar Works

Action	Title	Year	Authors
+	Counting factorisations of monomials over rings of integers modulo $N$	2017	Jonathan E. Hickman James Wright
+	Counting factorisations of monomials over rings of integers modulo $N$	2017	Jonathan Hickman James Wright
+	Sets of Linear Forms Which Are Hard to Compute	2021	Michael Kaminski Igor E. Shparlinski
+ PDF Chat	FACTORING POLYNOMIALS IN THE RING OF FORMAL POWER SERIES OVER ℤ	2012	Daniel Birmajer Juan B. Gil Michael D. Weiner
+	Solutions to polynomial congruenceswith variables restricted to a box	2024	Todd Cochrane Konstantinos Kydoniatis Craig Spencer
+	Factorisation of Polynomials	2022	Ian Stewart
+	Factorisation of Polynomials	2015
+	Two terms with known prime divisors adding to a power: REVISED	2020	Reese Scott Robert Styer
+	Solving Degenerate Sparse Polynomial Systems Faster	1999	J. Maurice Rojas
+	Solving Degenerate Sparse Polynomial Systems Faster	1998	J. Maurice Rojas
+	Two terms with known prime divisors adding to a power: REVISED with APPENDICES	2020	Reese Scott Robert Styer
+ PDF Chat	Reading Rational Univariate Representations on lexicographic Groebner bases	2024	Alexander Demin Fabrice Rouillier J. Gavilanes Ruiz
+	A simple scheme for polynomial factorization	1975	Tien D. Bui
+ PDF Chat	Factorization of polynomials over the field of rational numbers with polynomial complexity	2006	О. Н. Василенко
+ PDF Chat	Solving Bivariate Quadratic Congruences in Random Polynomial Time	1987	Leonard M. Adleman Dennis R. Estes Kevin S. McCurley
+	Remainder theorem and factorising polynomials	2017
+	Monomial congruences	1978	Melvyn B. Nathanson
+	Composite polynomials in linear recurrence sequences	2018	Clemens Fuchs Christina Karolus
+	On sets of linear forms of maximal complexity	2021	Michael Kaminski Igor E. Shparlinski Michel Waldschmidt
+ PDF Chat	On sets of linear forms of maximal complexity	2022	Michael Kaminski Igor E. Shparlinski Michel Waldschmidt

Works That Cite This (1)

Action	Title	Year	Authors
+ PDF Chat	The Fourier restriction and Kakeya problems over rings of integers modulo N	2018	Jonathan Hickman James Wright

Works Cited by This (15)

Action	Title	Year	Authors
+ PDF Chat	Introduction to Analytic Number Theory	1976	Tom M. Apostol
+	Regular sequences of power sums and complete symmetric polynomials	2011	Neeraj Kumar Ivan Martino
+ PDF Chat	Exponential sums: Questions by Denef, Sperber, and Igusa	2009	Raf Cluckers
+	ON THE NUMBER OF POINTS OF A HYPERELLIPTIC CURVE OVER A FINITE PRIME FIELD	1969	S. A. Stepanov
+	A Note on Simultaneous Congruences	1996	Trevor D. Wooley
+ PDF Chat	Igusa and Denef-Sperber conjectures on nondegenerate p-adic exponential sums	2007	Raf Cluckers
+	Report on Igusa's local zeta function	1991	Jan Denef
+	Exponential sums mod p(n) and Newton polyhedra	2001	Jan Denef Steven Sperber
+ PDF Chat	An abstract $L^2$ Fourier restriction theorem	2019	Jonathan Hickman James Wright
+ PDF Chat	The Fourier restriction and Kakeya problems over rings of integers modulo N	2018	Jonathan Hickman James Wright