On sums of integrals of powers of the zeta-function in short intervals

被引：0

作者：

Ivic, Aleksandar ^{[1
]}

机构：

[1] Univ Beogradu, Katedra Math RFG, Belgrade 11000, Serbia

来源：

MULTIPLE DIRICHLET SERIES, AUTOMORPHIC FORMS, AND ANALYTIC NUMBER THEORY | 2006年 / 75卷

关键词：

Riemann zeta-function; Mellin transforms; power moments;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The modified Mellin transform Z(k)(s) = integral(infinity)(1)vertical bar zeta(1/2+ix)vertical bar(2k)x(-s) dx, where k is an element of N is fixed, is used to obtain estimates for Sigma(R)(r=1) integral(tr-G) (tr+g) vertical bar zeta(1/2+it)vertical bar(2k) dt (T < t(1)<...< t(R)< 2T), where t(r+l) - t(r) >= G (r = 1,..., R - 1), T-epsilon <= G <= T1-epsilon. These results can be used to derive bounds for the moments of vertical bar zeta(1/2 +it)vertical bar.

引用

页码：231 / 242

页数：12

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