Explicit estimates for the Riemann zeta function

被引：19

作者：

Cheng, YF ^{[1
]}

Graham, SW ^{[1
]}

机构：

[1] Cent Michigan Univ, Dept Math, Mt Pleasant, MI 48859 USA

来源：

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 2004年 / 34卷 / 04期

关键词：

exponential sums; van der Corput's method; upper bound; the Riemann zeta function; explicit estimate;

D O I：

10.1216/rmjm/1181069799

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We apply van der Corput's method of exponential sums to obtain explicit upper bounds for the Riemann zeta function on the line sigma = 1/2. For example, we prove that if t > e, then \ zeta(1/2 + it)\ less than or equal to 3t(1/6)log t. These results will be used in an application on primes to short intervals [4].

引用

页码：1261 / 1280

页数：20

共 15 条

[1]

[Anonymous], 1993, BASIC ANAL NUMBER TH, DOI DOI 10.1007/978-3-642-58018-5

[2]

Chandrasekharan K., 1970, ARITHMETICAL FUNCTIO

[3]

CHENG YF, 2000, EXPLICIT ESTIMATE PR

[4]

CHENG YF, 1995, THESIS U GEORGIA

[5] An explicit upper bound for the Riemann zeta-function near the line σ=1 [J].

Cheng, YY .

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 1999, 29 (01) :115-140

[6]

Graham S.W., 1991, VANDERCORPUTS METHOD

[7] Explicit bounds on exponential sums and the scarcity of squarefree binomial coefficients [J].

Granville, A ;

Ramare, O .

MATHEMATIKA, 1996, 43 (85) :73-107

[8]

HUXLEY MN, 1993, P LOND MATH SOC, V66, P1

[9]

Ivic A., 1985, THEORY RIEMANN ZETA

[10]

Kress R, 1998, NUMERICAL ANAL

← 1 2 →