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.
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页码：1669 / 1677
页数：9
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