Counting factorisations of monomials over rings of integers modulo N

被引：0

作者：

Hickman, Jonathan ^{[1
]}

Wright, James ^{[2
,3
]}

机构：

[1] Univ St Andrews, Math Inst, St Andrews KY16 9SS, Fife, Scotland

[2] Univ Edinburgh, Maxwell Inst Math Sci, JCMB, Kings Bldg,Peter Guthrie Tait Rd, Edinburgh EH9 3FD, Midlothian, Scotland

[3] Univ Edinburgh, Sch Math, JCMB, Kings Bldg,Peter Guthrie Tait Rd, Edinburgh EH9 3FD, Midlothian, Scotland

来源：

JOURNAL DE THEORIE DES NOMBRES DE BORDEAUX | 2019年 / 31卷 / 01期

基金：

美国国家科学基金会;

关键词：

SUMS; SPERBER; DENEF;

D O I：

10.5802/jtnb.1079

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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 Z/p(alpha)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.

引用

页码：255 / 282

页数：28

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