On certain exponential sums over primes

被引：2

作者：

Maier, H. ^{[2
]}

Sankaranarayanan, A. ^{[1
]}

机构：

[1] TIFR, Sch Math, Mumbai 400005, Maharashtra, India

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

来源：

JOURNAL OF NUMBER THEORY | 2009年 / 129卷 / 07期

关键词：

Exponential sums; von Mangoldt function; Vaughan's identity; Difference operator; Holder's inequality; DIOPHANTINE APPROXIMATION; NUMBERS;

D O I：

10.1016/j.jnt.2009.01.018

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let f(x) be a real valued polynomial in x of degree k >= 4 with leading coefficient alpha. In this paper, we prove a non-trivial upper bound for the quantity vertical bar Sigma(p <= N)(log p)e(f(p))vertical bar whenever the leading coefficient alpha of f(x) is of type 1. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：1669 / 1677

页数：9

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