Moments of zeta and correlations of divisor-sums: IV

@article{Conrey2015MomentsOZ,
  title={Moments of zeta and correlations of divisor-sums: IV},
  author={Brian Conrey and Jonathan P. Keating},
  journal={Research in Number Theory},
  year={2015},
  volume={2},
  pages={1-24}
}
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 $$T^3$$T3… 
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Pair correlation and twin primes revisited
  • B. Conrey, J. Keating
  • Mathematics
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2016
TLDR
It is proved that the ratios conjecture and the arithmetic correlations conjecture imply the same result, which casts a new light on the underpinnings of the ratio conjecture.
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