The Fourier Restriction and Kakeya Problems over Rings of Integers Modulo N

被引：10

作者：

Hickman, Jonathan ^{[1
]}

Wright, James ^{[2
]}

机构：

[1] Univ Chicago, Dept Math, Eckhart Hall Room 414,5734 S Univ Ave, Chicago, IL 60637 USA

[2] Room 4621,James Clerk Maxwell Bldg,Kings Bldg, Edinburgh EH9 3FD, Midlothian, Scotland

来源：

DISCRETE ANALYSIS | 2018年

基金：

美国国家科学基金会;

关键词：

Fourier restriction; Kakeya; Congruence equations; EXTENSION-THEOREMS; RECENT PROGRESS; VECTOR-SPACES; FINITE; SETS; CURVES; CONJECTURES; TRANSFORMS; FAMILIES; SURFACES;

D O I：

10.19086/da.3682

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Fourier restriction phenomenon and the size of Kakeya sets are explored in the setting of the ring of integers modulo N for general N and a striking similarity with the corresponding euclidean problems is observed. One should contrast this with known results in the finite field setting.

引用

页码：1 / 54

页数：54

共 50 条

[1] Counting factorisations of monomials over rings of integers modulo N
Hickman, Jonathan
Wright, James
[J]. JOURNAL DE THEORIE DES NOMBRES DE BORDEAUX, 2019, 31 (01): : 255 - 282
[2] Class of TCM codes over rings of integers modulo-q
AhmadianAttari, M
Farrell, PG
[J]. ELECTRONICS LETTERS, 1996, 32 (18) : 1668 - 1670
[3] Instantiation of SMT Problems Modulo Integers
Echenim, Mnacho
Peltier, Nicolas
[J]. INTELLIGENT COMPUTER MATHEMATICS, 2010, 6167 : 49 - 63
[4] 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
[5] ON CODES OVER INTEGERS MODULO q
Durairajan, C.
Mahalakshmi, J.
[J]. ADVANCES AND APPLICATIONS IN DISCRETE MATHEMATICS, 2015, 15 (02): : 125 - 143
[6] A Gcd-Sum Function Over Regular Integers Modulo n
Toth, Laszlo
[J]. JOURNAL OF INTEGER SEQUENCES, 2009, 12 (02)
[7] UNIQUE FACTORIZATION IN INTEGERS MODULO N
BILLIS, M
[J]. AMERICAN MATHEMATICAL MONTHLY, 1968, 75 (05): : 527 - &
[8] AN ADDITION THEOREM ON THE INTEGERS MODULO N
LEMKE, P
KLEITMAN, D
[J]. JOURNAL OF NUMBER THEORY, 1989, 31 (03) : 335 - 345
[9] MATRIX FIELDS OVER INTEGERS MODULO M
BEARD, JTB
MCCONNEL, RM
[J]. NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1975, 22 (01): : A71 - A71
[10] MATRIX FIELDS OVER INTEGERS MODULO M
BEARD, JTB
MCCONNEL, RM
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1976, 14 (02) : 95 - 105

← 1 2 3 4 5 →