DECOUPLING, EXPONENTIAL SUMS AND THE RIEMANN ZETA FUNCTION

被引：156

作者：

Bourgain, J. ^{[1
]}

机构：

[1] Inst Adv Study, Princeton, NJ 08540 USA

来源：

JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY | 2017年 / 30卷 / 01期

关键词：

Riemann zeta function; exponential sums; decoupling;

D O I：

10.1090/jams/860

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We establish a new decoupling inequality for curves in the spirit of earlier work of C. Demeter and the author which implies a new mean value theorem for certain exponential sums crucial to the Bombieri-Iwaniec method as developed further in the work of Huxley. In particular, this leads to an improved bound (Formula Presented) for the zeta function on the critical line. © 2016 American Mathematical Society.

引用

页码：205 / 224

页数：20

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