Moments of zeta and correlations of divisor-sums: IV

被引：19
作者：
Conrey B. [1 ,2 ]
Keating J.P. [2 ]
机构：
[1] American Institute of Mathematics, 600 E. Brokaw Rd., San Jose, 95112, CA
[2] School of Mathematics, University of Bristol, Bristol
来源：
Research in Number Theory | / 2卷 / 1期
基金：
美国国家科学基金会; 欧盟地平线“2020”; 英国工程与自然科学研究理事会;
关键词：
Divisor Sums; Dirichlet Polynomials; Riemann Zeta-function; Convolution Sum; Circle Method;
D O I：
10.1007/s40993-016-0056-4
中图分类号：
学科分类号：
摘要：
In this series 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 begins 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 length up to T3 with divisor functions as coefficients. © 2016, The Author(s).
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