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

页码：292 / 350

页数：59

共 21 条

[11] Vaughan R. C., 1997, HARDY LITTLEWOOD MET
[12] Vaughan RC, 1997, ACTA ARITH, V79, P193
[13] A note on simultaneous congruences
Wooley, TD
[J]. JOURNAL OF NUMBER THEORY, 1996, 58 (02) : 288 - 297
[14] ON VINOGRADOV MEAN-VALUE THEOREM
WOOLEY, TD
[J]. MATHEMATIKA, 1992, 39 (78) : 379 - 399
[15] Some remarks on Vinogradov's mean value theorem and Tarry's problem
Wooley, TD
[J]. MONATSHEFTE FUR MATHEMATIK, 1996, 122 (03): : 265 - 273
[16] Wooley TD, 2014, PROCEEDINGS OF THE INTERNATIONAL CONGRESS OF MATHEMATICIANS (ICM 2014), VOL II, P505
[17] The cubic case of the main conjecture in Vinogradov's mean value theorem
Wooley, Trevor D.
[J]. ADVANCES IN MATHEMATICS, 2016, 294 : 532 - 561
[18] Multigrade efficient congruencing and Vinogradov's mean value theorem
Wooley, Trevor D.
[J]. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2015, 111 : 519 - 560
[19] VINOGRADOV'S MEAN VALUE THEOREM VIA EFFICIENT CONGRUENCING, II
Wooley, Trevor D.
[J]. DUKE MATHEMATICAL JOURNAL, 2013, 162 (04) : 673 - 730
[20] Vinogradov's mean value theorem via efficient congruencing
Wooley, Trevor D.
[J]. ANNALS OF MATHEMATICS, 2012, 175 (03) : 1575 - 1627

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