TY - JOUR
T1 - Moments of zeta and correlations of divisor-sums
T2 - IV
AU - Conrey, Brian
AU - Keating, Jon P
PY - 2016/12
Y1 - 2016/12
N2 - 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.
AB - 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.
U2 - 10.1007/s40993-016-0056-4
DO - 10.1007/s40993-016-0056-4
M3 - Article
VL - 2
JO - Research in Number Theory
JF - Research in Number Theory
SN - 2363-9555
M1 - 24
ER -