APPROXIMATING THE MAIN CONJECTURE IN VINOGRADOV'S MEAN VALUE THEOREM

被引：8
作者：
Wooley, Trevor D. [1 ]
机构：
[1] Univ Bristol, Sch Math, Univ Walk, Bristol BS8 1TW, Avon, England
来源：
MATHEMATIKA | 2017年 / 63卷 / 01期
关键词：
D O I：
10.1112/S0025579316000279
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We apply multigrade efficient congruencing to estimate Vinogradov's integral of degree k for moments of order 2s, establishing strongly diagonal behaviour for 1 <= s <= 1/2k(k+1) -1/3 k+o (k). In particular, as k -> infinity, we confirm the main conjecture in Vinogradov's mean value theorem for a proportion asymptotically approaching 100% of the critical interval 1 <= s <= 1/2k(k + 1).
引用
收藏
页码：292 / 350
页数：59
相关论文
共 21 条
  • [1] [Anonymous], 1949, J LOND MATH SOC
  • [2] [Anonymous], 1995, INT MATH RES NOTICES
  • [3] [Anonymous], 1948, P LOND MATH SOC
  • [4] [Anonymous], TRAY I MATH STEKLOFF
  • [5] [Anonymous], 1938, Q J MATH
  • [6] Arkhipov GI, 2004, DEGRUYTER EXPOS MATH, V39, P1, DOI 10.1515/9783110197983
  • [7] Proof of the main conjecture in Vinogradov's Mean Value Theorem for degrees higher than three
    Bourgain, Jean
    Demeter, Ciprian
    Guth, Larry
    [J]. ANNALS OF MATHEMATICS, 2016, 184 (02) : 633 - 682
  • [8] On Vinogradov's mean value theorem: strongly diagonal behaviour via efficient congruencing
    Ford, Kevin
    Wooley, Trevor D.
    [J]. ACTA MATHEMATICA, 2014, 213 (02) : 199 - 236
  • [9] Hardy G.H., 2008, An Introduction to the Theory of Numbers, VSixth
  • [10] Hua, 1965, ADDITIVE THEORY PRIM
123