# Higher correlations of divisor sums related to primes II: variations of the error term in the prime number theorem

```@article{Goldston2004HigherCO,
title={Higher correlations of divisor sums related to primes II: variations of the error term in the prime number theorem},
author={D. A. Goldston and C. Y. Yildirim},
journal={Proceedings of the London Mathematical Society},
year={2004},
volume={95}
}```
• Published 18 December 2004
• Mathematics
• Proceedings of the London Mathematical Society
We calculate the triple correlations for the truncated divisor sum λR(n). The λR(n) behave over certain averages just as the prime counting von Mangoldt function Λ(n) does or is conjectured to do. We also calculate the mixed (with a factor of Λ(n)) correlations. The results for the moments up to the third degree, and therefore the implications for the distribution of primes in short intervals, are the same as those we obtained (in the first paper with this title) by using the simpler…
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