EFFECTIVE l2 DECOUPLING FOR THE PARABOLA

被引：7
|
作者：
Li, Zane Kun [1 ]
机构：
[1] Indiana Univ, Dept Math, 831 East 3rd St, Bloomington, IN 47405 USA
来源：
MATHEMATIKA | 2020年 / 66卷 / 03期
关键词：
VINOGRADOVS; BOUNDS; PROOF;
D O I：
10.1112/mtk.12038
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We make effective l2Lp decoupling for the parabola in the range 4<p<6. In an appendix joint with Jean Bourgain, we apply the main theorem to prove the conjectural bound for the sixth-order correlation of the integer solutions of the equation x2+y2=m in an extremal case. This proves unconditionally a result that was proven in Bombieri and Bourgain [Int. Math. Res. Not. IMRN2015(11), 3343-3407] under the hypotheses of the Birch and Swinnerton-Dyer conjecture and the Riemann Hypothesis for L-functions of elliptic curves over Q.
引用
收藏
页码：681 / 712
页数：32
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