An optimal L2 autoconvolution inequality

被引:0
作者
White, Ethan Patrick [1 ]
机构
[1] Univ British Columbia, Dept Math, Room 121,1984 Math Rd, Vancouver, BC V6T 1Z2, Canada
来源
CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES | 2024年 / 67卷 / 01期
基金
加拿大自然科学与工程研究理事会;
关键词
Autoconvolution; Sidon set; additive energy; LOWER BOUNDS; SUPREMUM; NUMBER;
D O I
10.4153/S0008439523000565
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let F denote the set of functions f : [-1/2, 1/2] -> R->= 0 such that. f = 1. We determine the value of inf f is an element of F vertical bar vertical bar f * f vertical bar vertical bar(2)(2) up to a 4 center dot 10(-6) error, thereby making progress on a problem asked by Ben Green. Furthermore, we prove that a unique minimizer exists. As a corollary, we obtain improvements on the maximum size of B-h[g] sets for (g, h) is an element of{(2, 2), (3, 2), (4, 2), (1, 3), (1, 4)}.
引用
收藏
页码:108 / 121
页数:14
相关论文
共 18 条
  • [1] [Anonymous], GREEN 100 OPEN UNPUB
  • [2] Three convolution inequalities on the real line with connections to additive combinatorics
    Barnard, Richard C.
    Steinerberger, Stefan
    [J]. JOURNAL OF NUMBER THEORY, 2020, 207 : 42 - 55
  • [3] Bose R. C., 1962, Commentarii Mathematici Helvetici, V37, P141
  • [4] B-h[g] MODULAR SETS FROM B-h MODULAR SETS
    Caicedo, Yadira
    Gomez, Jhonny C.
    Trujillo, Carlos A.
    [J]. JP JOURNAL OF ALGEBRA NUMBER THEORY AND APPLICATIONS, 2015, 37 (01): : 1 - 19
  • [5] Bh[g] sequences
    Cilleruelo, J
    Jiménez-Urroz, J
    [J]. MATHEMATIKA, 2000, 47 (93-94) : 109 - 115
  • [6] Upper and lower bounds for finite Bh[g] sequences
    Cilleruelo, J
    Ruzsa, IZ
    Trujillo, C
    [J]. JOURNAL OF NUMBER THEORY, 2002, 97 (01) : 26 - 34
  • [7] ON SUPREMA OF AUTOCONVOLUTIONS WITH AN APPLICATION TO SIDON SETS
    Cloninger, Alexander
    Steinerberger, Stefan
    [J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2017, 145 (08) : 3191 - 3200
  • [8] The number of squares and Bh[g] sets
    Green, B
    [J]. ACTA ARITHMETICA, 2001, 100 (04) : 365 - 390
  • [9] A Numerical Note on Upper Bounds for B2[g] Sets
    Habsieger, Laurent
    Plagne, Alain
    [J]. EXPERIMENTAL MATHEMATICS, 2018, 27 (02) : 208 - 214
  • [10] Johnston G, 2022, AUSTRALAS J COMB, V83, P129