THE BEHAVIOUR IN SHORT INTERVALS OF EXPONENTIAL SUMS OVER SIFTED INTEGERS

被引：2

作者：

Maier, H. ^{[1
]}

Sankaranarayanan, A. ^{[2
]}

机构：

[1] Univ Ulm, Inst Number Theory & Probabil Theory, D-89069 Ulm, Germany

[2] Tata Inst Fundamental Res, Sch Math, Bombay 400005, Maharashtra, India

来源：

ILLINOIS JOURNAL OF MATHEMATICS | 2009年 / 53卷 / 01期

关键词：

NUMBER;

D O I：

10.1215/ijm/1264170842

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the Hardy-Littlewood approach to the Twin prime problem, which uses a certain exponential sum over prime numbers. We propose a conjecture on the behaviour of the exponential sum in short intervals of the argument. We first show that this conjecture implies the Twin prime conjecture. We then prove that an analogous conjecture is true for exponential sums over integers without small prime factors.

引用

页码：111 / 133

页数：23

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