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
收藏
页码：255 / 282
页数：28
相关论文
共 50 条
  • [1] The Fourier Restriction and Kakeya Problems over Rings of Integers Modulo N
    Hickman, Jonathan
    Wright, James
    [J]. DISCRETE ANALYSIS, 2018, : 1 - 54
  • [2] Counting Integers Representable as Images of Polynomials Modulo n
    Arias, Fabian
    Borja, Jerson
    Rubio, Luis
    [J]. JOURNAL OF INTEGER SEQUENCES, 2019, 22 (06)
  • [3] Class of TCM codes over rings of integers modulo-q
    AhmadianAttari, M
    Farrell, PG
    [J]. ELECTRONICS LETTERS, 1996, 32 (18) : 1668 - 1670
  • [4] Counting Integers Representable as Sums of k-th Powers Modulo n
    Arias, Fabian
    Borja, Jerson
    Anaya, Samuel
    [J]. JOURNAL OF INTEGER SEQUENCES, 2023, 26 (08)
  • [5] The diameters of commuting graphs of linear groups and matrix rings over the integers modulo m
    Giudici, Michael
    Pope, Aedan
    [J]. AUSTRALASIAN JOURNAL OF COMBINATORICS, 2010, 48 : 221 - 230
  • [6] ON CODES OVER INTEGERS MODULO q
    Durairajan, C.
    Mahalakshmi, J.
    [J]. ADVANCES AND APPLICATIONS IN DISCRETE MATHEMATICS, 2015, 15 (02): : 125 - 143
  • [7] On counting rings of integers as Galois modules
    Agboola, A.
    [J]. JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2012, 663 : 1 - 31
  • [8] A Gcd-Sum Function Over Regular Integers Modulo n
    Toth, Laszlo
    [J]. JOURNAL OF INTEGER SEQUENCES, 2009, 12 (02)
  • [9] UNIQUE FACTORIZATION IN INTEGERS MODULO N
    BILLIS, M
    [J]. AMERICAN MATHEMATICAL MONTHLY, 1968, 75 (05): : 527 - &
  • [10] AN ADDITION THEOREM ON THE INTEGERS MODULO N
    LEMKE, P
    KLEITMAN, D
    [J]. JOURNAL OF NUMBER THEORY, 1989, 31 (03) : 335 - 345
12345