# Moments of zeta and correlations of divisor-sums: V

## TL;DR

This paper advances the understanding of the moments of the Riemann zeta-function by analyzing Type II sums using circle method techniques to derive precise asymptotics for divisor sum correlations.

## Contribution

It completes the analysis of Type II sums, providing a comprehensive framework for calculating lower order terms in zeta moments using divisor correlations.

## Key findings

- Derived asymptotic formulas for divisor sum correlations
- Completed the analysis of Type II sums in zeta moments
- Enhanced methods for calculating moments of the zeta-function

## 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.