Moments of zeta and correlations of divisor-sums: V

被引:18
作者
Conrey, Brian [1 ,2 ]
Keating, Jonathan P. [2 ]
机构
[1] Amer Inst Math, 360 Portage Ave, Palo Alto, CA 94306 USA
[2] Univ Bristol, Sch Math, Bristol BS8 1TW, Avon, England
基金
英国工程与自然科学研究理事会; 美国国家科学基金会;
关键词
RANDOM-MATRIX THEORY; RIEMANN ZEROS;
D O I
10.1112/plms.12196
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this series of papers we examine the calculation of the 2kth moment and shifted moments of the Riemann zeta-function on the critical line using long Dirichlet polynomials and divisor correlations. The present paper completes the general study of what we call Type II sums which utilize a circle method framework and a convolution of shifted convolution sums to obtain all of the lower order terms in the asymptotic formula for the mean square along [T,2T] of a Dirichlet polynomial of arbitrary length with divisor functions as coefficients.
引用
收藏
页码:729 / 752
页数:24
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