Moments of zeta and correlations of divisor-sums: V

Abstract

In this series of papers we examine the calculation of the $2k$th 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.

Revised version; accepted in PLMS

References in corpus (1)

• Averages of ratios of the Riemann zeta-function and correlations of divisor sums

Cited by in corpus (10)

• Moments of quadratic twists of elliptic curve L-functions over function fields
• On the moments of the moments of $\zeta (1/2+it)$
• Maxima of log-correlated fields: some recent developments
• Spectral Moment Formulae for $GL(3)\times GL(2)$ $L$-functions III: The Twisted Case
• Hierarchical Structure in the Trace Formula
• Averages of long Dirichlet polynomials
• Conjectures for the Integral Moments and Ratios of L-functions in Even characteristic
• Mean values of long Dirichlet polynomials with divisor coefficients
• Twin prime correlations from the pair correlation of Riemann zeros
• Spectral Moment Formulae for $GL(3)\times GL(2)$ $L$-functions II: The Eisenstein Case